{"id":246189,"date":"2025-03-10T16:00:43","date_gmt":"2025-03-10T08:00:43","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=246189"},"modified":"2025-06-13T18:27:38","modified_gmt":"2025-06-13T10:27:38","slug":"7-steps-to-solving-math-questions-involving-prime-numbers","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/7-steps-to-solving-math-questions-involving-prime-numbers\/","title":{"rendered":"7 Steps To Solving Math Questions Involving Prime Numbers"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.16″ global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” z_index_tablet=”500″ custom_css_main_element=”sub,||sup {||font-size: 75%;||line-height: 0;||position: relative;||vertical-align: baseline;||}||sup {||top: -0.5em;||}||sub {||bottom: -0.25em;||}” global_colors_info=”{}”]<\/p>\n

Introduction<\/strong><\/p>\n

Welcome back to another Secondary 1 Math<\/a> blog post!<\/p>\n

In this article, I will be giving you a step-by-step guide to answering a tricky Prime Numbers question involving a cuboid.<\/p>\n

I noticed that students tend to lose points when answering this question because they missed an important keyword in the question.<\/p>\n

Keep on reading if you want to find out what this keyword is and avoid making the same mistake!<\/p>\n

<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Prime Numbers Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. Algebra: How To Expand Linear Expressions<\/b><\/a><\/li>\n
  2. Estimation & Approximation: How To Estimate Using Given Information<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    We are going to solve this question using the Prime Factorisation Method<\/strong>.<\/p>\n

    But first, let us read the question together.<\/p>\n

    Step 1\ufe0f\u20e3: Identify The Keywords<\/strong><\/h2>\n

    There are 140 pieces of 3 cm cubes<\/strong>.<\/p>\n

    In the very first sentence, there are actually two important pieces of information:<\/p>\n

    1\ufe0f\u20e3\u00a0140 pieces of cubes<\/p>\n

    2\ufe0f\u20e3 3 cm cubes<\/p>\n

    \n

    \ud83d\udce6<\/span>\u00a0What Does 3 CM Cubes Mean?<\/span> <\/strong>\ud83d\udce6<\/span><\/p>\n

    It means that when you\u2019re building the cube, each side of the cube is 3 cm.<\/p>\n<\/blockquote>\n

    \"How<\/p>\n

     <\/p>\n

    In this sense, the question is a bit tricky because we are not dealing with 1 cm cubes. We are now dealing with 3 cm cubes.<\/p>\n

    What about the 140 pieces? What does it mean?<\/p>\n

    Because we are going to make a cuboid, like the one in the diagram above, 140 pieces<\/strong> would make up the volume<\/strong>.<\/p>\n

    Step 2\ufe0f\u20e3: Use The Prime Factorisation Method To Break Up The Volume<\/span><\/strong><\/h2>\n

    For the next step, we are going to break up 140 using the Prime Factorisation Method<\/span><\/strong>.<\/p>\n

    \"How<\/p>\n

    However, I like to break it up into individual factors so that I can see which numbers make up 140.<\/p>\n

    \"How<\/p>\n

    Step 3\ufe0f\u20e3: Identify The Perimeter<\/strong><\/h2>\n

    Now, what\u2019s the next clue?<\/p>\n

    The next clue is the perimeter of the base!<\/p>\n

    \"The<\/p>\n

    \u200b<\/p>\n

    Some of you may be asking, \u201cWhere is the base?\u201d<\/p>\n

    The base is actually at the top, which we highlighted in green below.<\/p>\n

    The perimeter is the 2 lengths (L) and 2 breadths (B) that we marked with green below.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    Step 4\ufe0f\u20e3: Find The Number Of Cubes Along The Perimeter<\/span><\/strong><\/h2>\n

    The 72 cm refers to the perimeter, but does it mean that there are 72 cubes along the lengths and the breadths?<\/p>\n

    The answer is no because we are dealing with 3 cm cubes. So there shouldn’t be 72 cubes.<\/p>\n

    Let us compute the number of cubes along the perimeter.<\/p>\n

    \"How<\/p>\n

    Step 5\ufe0f\u20e3: Compute For The Number Of Cubes Along The Breadth & Length<\/span><\/strong><\/h2>\n

    Now, that we know that there are 24 cubes along the perimeter, we can narrow this down to:<\/p>\n

    \"How<\/p>\n

    How do we use the number 12 to help us find the two possible heights of the cuboid?<\/p>\n

    Where is the height of the cuboid? Let us first label it. We are going to use the letter H to label the height.<\/p>\n

    \"How<\/p>\n

    For labelling purposes, we’re going to follow these:<\/p>\n

    \"How<\/p>\n

    \n

    \ud83e\udd14\u00a0Why Do We Need NL & NB?<\/strong> \ud83e\udd14<\/p>\n

    We cannot say that length + breadth = 12, because 12 is the number of cubes<\/strong>, not<\/strong> the actual perimeter<\/strong>.<\/p>\n<\/blockquote>\n

    So, it means that NL + NB = 12 cubes.<\/p>\n

    How is this information useful to us?<\/p>\n

    Because if we can guess the number of cubes along the length and breadth, which are the possible sums of 12, we can figure out our two possible heights.<\/p>\n

    <\/p>\n

    Step 6\ufe0f\u20e3<\/span>: Guess & Check<\/span><\/strong><\/h2>\n

    Therefore, our next step is to start guessing. We\u2019ll do that by drawing a table.<\/p>\n

    In the first column, let\u2019s write down NL or the number of cubes along the length.<\/p>\n

    For the second column, let\u2019s write down NB or the number of cubes along the breadth.<\/p>\n

    Finally, in the third column, let\u2019s write down \u201cCheck,\u201d which means that we\u2019re going to use this column to either accept or reject the possible combinations of NL and NB.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    Remember that we have a total of 12. How do we get a sum of 12?<\/p>\n

    Can I begin with 0 and 12? Definitely not because I cannot have 0 cubes making up the length or the breadth!<\/p>\n

    So the smallest number will be 1. If one side is 1, we need the other side to have 11 cubes.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    Let us first list down all the possible combinations.<\/p>\n

    \"How<\/p>\n

    So there are 6 total possible combinations.<\/p>\n

    The question gave us a clue that there are only two possible heights, which means that out of the total of six combinations, we need to eliminate four of them.<\/p>\n

    Which ones do we eliminate? This is where we are going to use the prime factorisation of 140 that we solved earlier.<\/p>\n

    \"How<\/p>\n

    \u200bSo if you look at the first combination, do you think it’s possible to have 11 cubes along the breadth? <\/p>\n

    \"How<\/p>\n

    \u200b<\/p>\n

    Remember that 140 makes up the volume.<\/p>\n

    So 140 or 2 x 2 x 5 x 7 is actually the length x breadth x height.<\/p>\n

    If we are going to get 11 cubes along the breadth, I have to check my factors of 140. Do you think it’s possible to get 11 cubes? The answer is no.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    Now let’s take a look at combination 3.<\/p>\n

    Is it possible to get 3 cubes along the length? Again, if you look at the factors of 140, the answer is no, because we cannot find 3 anywhere in the factors of 140.<\/p>\n

    \"How<\/p>\n

    Now, let us look at combination 6.<\/p>\n

    \"How<\/p>\n

    How do we get 6? 6 is actually 2 x 3. And because we cannot have a 3 in our factors of 140, this is also not a possible answer!<\/p>\n

    \"How<\/p>\n

    This leaves us with 3 possible combinations \u2014 numbers 2, 4, and 5. However, we only need 2 possible heights so we have to eliminate one of them.<\/p>\n

    Let us look at combination 4!<\/p>\n

    We can make up 4 from our factors of 140 because there is 2 x 2, which gives us 4.<\/p>\n

    \"How<\/p>\n

    But 8 is actually 2 x 2 x 2. I need three sets of 2s to make up 8, which is impossible because we are only left with 5 and 7. We no longer have an extra 2.<\/p>\n

    So combination number 4 is also out of the question!<\/p>\n

    \"How<\/p>\n

    This is good news because we are only left with 2 combinations \u2014 2 and 5.<\/p>\n

    So let’s check combination 2 first!<\/p>\n

    Can the number of cubes along the breadth be 10? Yes, because I have 2 and 5, which are factors of 140. For the number of cubes along the length, we have 2, which is also a factor of 140.<\/p>\n

    So this is possible!<\/p>\n

    \"How<\/p>\n

    What about 5 and 7 for combination 5?<\/p>\n

    The numbers 5 and 7 are also factors of 140. So this is another possible combination!<\/p>\n

    \"How<\/p>\n

    Step 7\ufe0f\u20e3: Find The Possible Heights<\/span><\/strong><\/h2>\n

    We can finally answer the question! How are we going to do that?<\/p>\n

    Recall that we are dealing with 3 cm cubes. So, the first step is to find the two possible heights.<\/p>\n

    So I’m going to label the first height as H1, which means that if I have 140 cubes, in order to find the height, this would be the volume divided by the base area.<\/p>\n

    So if I take 140 divided by base area which are 2 and 10, I will get 7.<\/p>\n

    \"How<\/p>\n

    But recall that it’s not the actual height because we are not dealing with 1 cm cubes. We are dealing with 3 cm cubes.<\/p>\n

    So it will be 7 x 3, which is 21 cm. So the first possible answer is 21.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    <\/p>\n

    The second possible answer would be the volume, 140 divided by base area (combination 5), which is 5 x 7. This will give us 4 cubes.<\/p>\n

    But again, each cube is 3 cm in length, so we will multiply it by 3. Therefore, our answer will be 12 cm.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Suggested Answer<\/span><\/h2>\n

    H<\/em>1<\/sub> = 21 cm<\/em><\/p>\n

    H<\/em>2<\/sub> = 12 cm<\/em>\u200b\u200b<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/h2>\n

    Conclusion<\/span>
    <\/h2>\n

    I hope that after reading this S1 Math blog post, you have learned the importance of reading the question carefully and taking note of the keywords.<\/p>\n

    Some might assume that the perimeter of the base is made up of 72 cubes. But the question states that the cuboid is made up of 3 cm cubes so the perimeter of the base cannot be made up of 72 cubes.<\/p>\n

    Remember to follow the 7 steps that we did to solve similar questions in future!<\/p>\n

    \n

    Step 1\ufe0f\u20e3: Identify The Keywords<\/p>\n

    Step 2\ufe0f\u20e3: Use The Prime Factorisation Method To Break Up The Volume<\/p>\n

    Step 3\ufe0f\u20e3: Identify The Perimeter<\/p>\n

    Step 4\ufe0f\u20e3: Find The Number Of Cubes Along The Perimeter<\/p>\n

    Step 5\ufe0f\u20e3: Compute For The Number Of Cubes Along The Breadth & Length<\/p>\n

    Step 6\ufe0f\u20e3: Guess & Check<\/p>\n

    Step 7\ufe0f\u20e3: Find The Possible Heights<\/p>\n<\/blockquote>\n

    See you in the next S1 Math<\/a> blog post!<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row disabled_on=”off|off|off” admin_label=”Math GAP” _builder_version=”4.21.0″ custom_margin=”0px||” custom_padding=”0px||” global_module=”244058″ saved_tabs=”all” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_divider color=”#898989″ admin_label=”Divider” _builder_version=”4.21.0″ locked=”off” global_colors_info=”{}”][\/et_pb_divider][et_pb_image src=”https:\/\/thepiquelab.com\/blog\/wp-content\/uploads\/2024\/03\/The-Pique-Lab-Grade-Accelerator-Programme.-CTA.png” align=”center” _builder_version=”4.21.0″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” text_text_color=”#333333″ text_font_size=”18px” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

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    In this article, we\u2019ll be discussing how to solve this Secondary 1 Math question on Prime Numbers..<\/p>\n","protected":false},"author":41,"featured_media":246191,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[59,77],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246189"}],"collection":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/comments?post=246189"}],"version-history":[{"count":7,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246189\/revisions"}],"predecessor-version":[{"id":246574,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/246189\/revisions\/246574"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/246191"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=246189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=246189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=246189"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=246189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}