{"id":10865,"date":"2026-11-02T02:02:53","date_gmt":"2026-11-02T02:02:53","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10865"},"modified":"2026-11-02T02:02:53","modified_gmt":"2026-11-02T02:02:53","slug":"introduction-to-factors-multiples","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/introduction-to-factors-multiples\/","title":{"rendered":"Introduction To Factors & Multiples"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit<\/strong>: Number System<\/h2>\n

Chapter<\/strong>: Introduction to Factors & Multiples<\/h3>\n

Reference<\/strong>: \u2013 Factors and Their Meaning, Multiples and Their Meaning, Relationship Between Factors and Multiples, Finding Factors of a Number, Finding Multiples of a Number, Even and Odd Numbers, Prime and Composite Numbers, Perfect Numbers<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/p>\n

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  • Meaning of Factors & How to Find Them<\/li>\n
  • Meaning of Multiples & How to Find Them<\/li>\n
  • Relationship Between Factors and Multiples<\/li>\n
  • Even and Odd Numbers<\/li>\n
  • Prime and Composite Numbers<\/li>\n
  • Perfect Numbers<\/li>\n
  • Real-Life Applications of Factors & Multiples<\/li>\n<\/ul>\n

    Factors & Multiples<\/strong><\/p>\n

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    Factors<\/strong><\/p>\n

    The numbers that we multiply to get a certain number are called its factors.<\/strong><\/p>\n

    For example,<\/strong>2 \u00d7 5 = 10<\/p>\n

    Here, both 2 and 5 are factors of 10.<\/p>\n

    In the above example, we can see that 2 and 5 both can completely divide 10 without leaving any remainder.<\/p>\n

    So, we can say that factors<\/strong> are \u201call of those numbers\u201dthat can divide \u201ca given number\u201d completely (meaning \u2013 the remainder should be 0 after division).<\/p>\n

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    Example-<\/strong>Write all the factors of 12.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 Factors of 12 are 1, 2, 3, 4, 6 and 12 as each of these can completely divide 12.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><\/p>\n

    Multiples<\/strong><\/p>\n

    Are the numbers <\/strong>we get when we multiply any counting number by an integer, andare called its multiples.<\/strong><\/p>\n

    For example,<\/strong>6 \u00d7 5 = 30<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6 \u00d7 7 = 42<\/p>\n

    Here, both 30 and 42 are multiples of 6.<\/p>\n

    \u00a0<\/p>\n

    We can see in the above example, 30 is a multiple of 5 too and 42 is a multiple of 7 too. So, we can say 30 is a common multiple<\/strong> of 5 and 6, and 42 is a common multiple of 6 and 7.<\/p>\n

    \u00a0<\/p>\n

    Example<\/strong>– Write 5 multiples of 12.<\/p>\n

    Multiples of 12 are 12, 24, 36, 48, 60.<\/p>\n

    Do Remember<\/strong><\/p>\n

    #Factors and multiples are inter-related with each other. Every number is a factor of its multiple.<\/p>\n

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    Example<\/strong>– If 18 is a multiple of 6, then 6 is a factor of 18.<\/p>\n

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    Prime Factorization<\/strong><\/p>\n

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    When we express a composite number as a product of prime numbers, it is called prime factorization.<\/strong> The set of prime numbers are called the prime factors<\/strong> of the given number.<\/p>\n

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    Example-<\/strong>Let us take a number 24.<\/p>\n

    Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.<\/p>\n

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    Out of these factors, the prime factors are 2 and 3.<\/p>\n

    Now, let us express 24 as a product of its prime factors.<\/p>\n

    \u00a0<\/p>\n

    So, 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3<\/p>\n

    \u00a0<\/p>\n

    Thus, prime factorization<\/strong> is expressing a number as a product of its prime factors.<\/p>\n

    \u00a0<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

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    Method 1: Factor Tree Method<\/strong><\/p>\n

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    • In this method, we start splitting the given numbers into factors until we cannot split anymore.<\/li>\n<\/ul>\n

      \u00a0<\/p>\n

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      • The factor that cannot be split anymore i.e. the prime factor is carried down as it is whereas the composite factor is further split in the next step till it becomes prime.<\/li>\n<\/ul>\n

        \u00a0<\/p>\n

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        • Then, all the prime factors of the number are stated in product form to define the actual number.<\/li>\n<\/ul>\n

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          • The standard way of listing the prime factors is from smallest number to the largest one.<\/li>\n<\/ul>\n

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            Example <\/strong>\u2013 Find the prime factorization of 60.<\/p>\n

            \"\"<\/p>\n

            Source: Kapdec.com<\/p>\n<\/div>\n

            Thus, 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5<\/p>\n

            \u00a0<\/p>\n

            #The given number can be treated as a stem while its breakup into prime factors can be treated as its branches.<\/p>\n

            Method 2:Short Division Method<\/strong><\/p>\n

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            • In this method, first we divide the given number by a smallest prime number which completely divides the given number.<\/li>\n<\/ul>\n

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              • Then, we divide the quotient again with a smallest prime number or the next smallest prime number which can completely divide the number.<\/li>\n<\/ul>\n

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                • We repeat the above step again and again, till the quotient becomes 1.<\/li>\n<\/ul>\n

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                  • The product of all the divisors that we got through the above step gives us the number itself and are thereby the prime factors of the number.<\/li>\n<\/ul>\n

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                    Example <\/strong>\u2013 Find the prime factorization of 72.<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/p>\n

                    \"\"<\/p>\n

                    Source: Kapdec.com<\/p>\n<\/div>\n

                    Thus, 72 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3<\/p>\n

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                    <\/p>\n