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Module 3 (M3) - Number - Multiples and factors

Part of MathsM3: Number

Multiples and factors

  • Numbers that divide exactly into another number, leaving no remainder, are called factors.

  • A prime number has exactly two factors, itself and 1.

  • The only even prime number is 2.

  • The number 1 is not prime as it only has one factor.

  • The highest common factor (HCF) is the highest number which is a factor of both numbers.

  • The lowest common multiple (LCM) is the lowest multiple common to both numbers.

Prime factors are prime numbers that divide exactly into a number.

Every non-prime number can be expressed as a product of prime factors,for example:

30 = 2x3x5 and 77 = 7x11

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Factor tree method

Write 24 as the product of its prime factors

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  1. 24<4 6 or 24 <3 8

    You could choose any factor pair to start.

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Ladder method

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  1. 24/2=12

    Start with 24 and divide by a prime number which is a factor

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Example

Express 105 as a product of its prime factors.

Question

Write 84 as a product of its prime factors in index form.

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Highest common factor and lowest common multiple

Intersection

Example

Find the highest common factor and the lowest common multiple of 105 and 84.

Solution

  • Begin by writing each number as a product of their prime factors.

    • 105 = 3 x 5 x 7
    • 84 = 22 x 3 x 7

  • Place the factors onto a Venn diagram with the common factors in the centre.

Venn diagram 105 - factors 3 5 7 & 84 2x2 x 3 x 7
Answer:
  • The highest common factor is the product of the numbers in the intersection.
    3x7=21
  • The lowest common multiple is the product of all the numbers.
    5x3x7x2x2=420

Question

What is the highest common factor (HCF) of 50 and 90?

Question

What is the lowest common multiple (LCM) of 30 and 24?

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Test yourself

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More on M3: Number

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