{"id":245326,"date":"2024-08-12T16:00:13","date_gmt":"2024-08-12T08:00:13","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=245326"},"modified":"2025-06-16T13:11:56","modified_gmt":"2025-06-16T05:11:56","slug":"highest-common-multiple-2-methods-to-solve-hcf-word-problems","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/highest-common-multiple-2-methods-to-solve-hcf-word-problems\/","title":{"rendered":"Highest Common Multiple: 2 Methods To Solve HCF Word Problems"},"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=”||||||||” hover_enabled=”0″ 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=”{}” sticky_enabled=”0″]<\/p>\n

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

Let\u2019s do a quick recap on the Highest Common Multiple.<\/p>\n

\n

\ud83d\udd0e What Is HCF?<\/strong> \ud83d\udd0e<\/p>\n

The Highest Common Factor (HCF) is the largest number that can divide given numbers without leaving a remainder.<\/p>\n<\/blockquote>\n

In this blog post, I will be sharing with you two methods you can use to find the HCF quickly and accurately \u2014 the Prime Factorisation and Ladder Methods!<\/p>\n

<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Estimation & Approximation Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. [Secondary 2 Math Explainer Video] Direct Proportion: Finding The Relationship Between A & H<\/b><\/a><\/li>\n
  2. Algebra: How To Simplify Algebraic Fractions<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    <\/h2>\n

    Let\u2019s Find The Keywords In This Question<\/span><\/h2>\n

    What are the keywords in the question?<\/p>\n

    First, the number of each fruit that Chloe has to pack.<\/p>\n

    Chloe needs to pack 120 apples<\/strong><\/span>, 150 oranges<\/strong><\/span>, and 108 mangoes<\/span>.<\/strong><\/p>\n

    Next, she needs to pack them into identical boxes so that each type of fruit is equally distributed<\/strong>.<\/p>\n

    \"The<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Let’s Take A Look At Part (A)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    First, what do we need to solve to answer this question? We need to find the HCF<\/strong> of 120<\/strong>, 150<\/strong>, and 108<\/strong>!<\/p>\n

    There are two ways that we can find the HCF \u2014 the Prime Factorisation Method<\/strong> and the Ladder Method<\/strong>!<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Finding The HCF Using The Prime Factorisation Method<\/span>
    <\/h2>\n

    Begin by writing down the three numbers \u2014 120, 150, and 108.<\/p>\n

    Next, break them down into prime numbers.<\/p>\n

    \n

    \ud83d\udca1 Tip When Breaking Down Numbers Into Prime Numbers <\/strong>\ud83d\udca1<\/p>\n

    If you tend to forget what prime numbers to use, always make it a habit to write down at least the first five prime numbers in a corner.
    The first five prime numbers are 2, 3, 5, 7, and 11.<\/p>\n<\/blockquote>\n

    <\/p>\n

    \"How<\/p>\n

    Take 120 and key it into your calculator.<\/p>\n

    Divide it by 2, which is the smallest prime number, and you will get 60.<\/p>\n

    Next, divide 60 by 2. It will give you 30.<\/p>\n

    Divide 30 by 2 again and you will get 15.<\/p>\n

    Now, divide 15 by 3 and you will get 5, which are prime numbers<\/p>\n

    Collect all the prime numbers and list them down.<\/p>\n

    \"How<\/p>\n

    Key in the entire expression into your calculator and check if you got 120. If not, then something must be wrong.<\/p>\n

    2 x 2 x 2 x 3 x 5 is indeed 120 so we can now write it down in index notation form.<\/p>\n

    We will get 23<\/sup>\u00a0x 3 x 5.<\/p>\n

    \"How<\/p>\n

    Next, we are going to repeat the same process with 150.<\/p>\n

    Key 150 into your calculator and divide it by 2. You will get 75.<\/p>\n

    Now, divide 75 by 3 and you will get back 25.<\/p>\n

    We know that 5 x 5 is equal to 25. Now, write down all the prime numbers.<\/p>\n

    \"How<\/p>\n

    Let\u2019s double-check: 2 x 3 x 5 x 5 = 150!<\/p>\n

    We\u2019ve confirmed that we will get back 150 so we can now write it down in index notation.<\/p>\n

    2 x 3 x 52<\/sup><\/p>\n

    \"How<\/p>\n

    Let us repeat the process for 108.<\/p>\n

    Key in 108 into your calculator and divide it by 2. You will get 54.<\/p>\n

    Next, 54 is divisible by 2. You will get 27.<\/p>\n

    We know that 27 is divisible by 3 and you will get 9.<\/p>\n

    Finally, 9 is a product of 3 x 3.<\/p>\n

    Write down all the prime numbers.<\/p>\n

    \"How<\/p>\n

    2 x 2 x 3 x 3 x 3 = 108<\/p>\n

    Finally, write it down in index notation and you will get 22<\/sup> x 33<\/sup>.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    Now, let us look for the HCF by looking at the prime numbers that the three given numbers have in common.<\/p>\n

    We have the 2s and 3s because 108 does not have a 5.<\/p>\n

    <\/p>\n

    \"\"<\/p>\n

    Check how many 2s and 3s are common among the three numbers.<\/p>\n

    2 x 3 = 6<\/p>\n

    Our HCF is 6<\/strong>.<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/h2>\n

    Suggested Answer For Part (A)<\/span>
    <\/h2>\n

    The HCF refers to the largest number of boxes that can be packed.<\/p>\n

    Therefore, Chloe can pack 6 boxes<\/strong>.<\/p>\n

    <\/p>\n

    Let\u2019s Take A Look At Part (B)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Now, let us compute the total number of fruits in each box.<\/p>\n

    To do that, take the number of each type of fruit and divide it by 6.<\/p>\n

    120 apples<\/span> \u00f7 6 = 20 apples<\/span><\/p>\n

    150 oranges<\/span> \u00f7 6 = 25 oranges<\/span><\/p>\n

    108 mangoes<\/span> \u00f7 6 = 18 mangoes<\/span><\/p>\n

    But this is not the end, because the question is asking for the total number<\/strong> of fruits in each box.<\/p>\n

    20 apples<\/span> + 25 oranges<\/span> + 18 mangoes<\/span> = 63 fruits<\/strong>!<\/p>\n

    <\/h2>\n

    Suggested Answer For Part (B)<\/span>
    <\/h2>\n

    There are 63 fruits<\/strong> in the boxes.<\/p>\n

    <\/p>\n

    Finding The Answers Using The Ladder Method<\/span>
    <\/h2>\n

    In this question, the Ladder Method has a slight advantage because you will find the answers for (a) and (b) in one working.<\/p>\n

    Begin by drawing your ladder.<\/p>\n

    \"How<\/p>\n

    All these numbers are divisible by 2, to get 60, 75, and 54.<\/p>\n

    \"How<\/p>\n

    We cannot divide the numbers by 2 because 75 is not an even number. So, let us divide the numbers by 3. We will get 20, 25, and 18.<\/p>\n

    \"How<\/p>\n

    Finally, when you arrive at this last set of numbers, you\u2019ll realise that they no longer have anything in common so we can now stop.<\/p>\n

    \"How<\/p>\n

    2 and 3 make up your HCF.<\/p>\n

    2 x 3 = 6<\/p>\n

    The HCF<\/strong> is 6<\/strong> and it is also the answer for part (a) which is looking for the number of boxes that can be packed.<\/p>\n

    Now, how are we going to find the answer for part (b)? It is actually in the working. Can you spot where it is? It is in the last row!<\/p>\n

    For the ladder method, the last row will give you the number of each type of fruit, so all you have to do for part (b) is to find the total.<\/p>\n

    20 apples<\/span> + 25 oranges<\/span> + 18 mangoes<\/span> = 63 fruits<\/strong>!<\/p>\n

    <\/p>\n

    <\/p>\n

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

    I hope that after reading this blog post, you have gained more confidence in approaching Secondary Math word problems that involve the Highest Common Factor (HCF).<\/p>\n

    As we\u2019ve discussed, you can use either the Prime Factorisation Method or the Ladder Method.<\/p>\n

    Also, remember to read the question thoroughly to ensure that you are solving for the correct concept. Many students often get confused between HCF and LCM (Lowest Common Multiple).<\/p>\n

    Practise more of our other Estimation & Approximation\u00a0questions!<\/p>\n

    Keep a lookout for more Math blog posts!<\/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

    If you like our methodology, we’ve some ongoing weekly Math classes:<\/p>\n

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    In this article, we’ll be discussing how to use the Prime Factorisation and Ladder Method question on Highest Common Multiple to solve this Secondary 1 Math Estimation & Approximation question.<\/p>\n","protected":false},"author":41,"featured_media":245328,"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":[59,72],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/245326"}],"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=245326"}],"version-history":[{"count":5,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/245326\/revisions"}],"predecessor-version":[{"id":246587,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/245326\/revisions\/246587"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/245328"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=245326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=245326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=245326"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=245326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}