- A
**common factor**of two numbers is a number that both numbers can be divided by- 1 is a common factor of any two numbers

- To find
**common factors**you can write out the**factors**of each number and identify the numbers that**appear in both lists**- The
**factors of a common factor**of two numbers will**also be common factors**- 6 is a common factor of 24 and 30
- Therefore 1, 2, 3, 6 are also common factors of 24 and 30

- The
- The
**highest common factor**is the largest common factor between two numbers- This is useful when simplifying fractions or factorising expressions

- Write each number as a
**product of its prime factors** - Find the prime factors that are
**common**to both numbers- Be careful with how many times a prime factor appears
- 12 = 2 × 2 × 3 and 10 = 2 × 5
- So
**only one**of the 2s is a common prime factor

- Be careful with how many times a prime factor appears
**Multiply**the common prime factors together- Using a
**Venn diagram**can help- Put the common prime factors in the centre
- Put the other prime factors in the relevant circles
- The HCF is the product of
**all the numbers**in the**centre**

Find the highest common factor of 42 and 90.

Write as a product of prime factors

42 = 2 × 3 × 7

90 = 2 × 3 × 3 × 5

Write the prime factors in a Venn diagram if needed.

Multiply the common prime factors.

HCF = 2 × 3

**HCF = 6**

- A
**common multiple**of two numbers is a number that appears in both of their times tables- The product of the two numbers is always a common multiple

- To find
**common multiples**you can write out the**multiples**of each number and identify the numbers that**appear in both lists**- The
**multiples of a common multiple**of two numbers will**also be common multiples**- 60 is a common multiple of 12 and 10
- Therefore 60, 120, 180, 240, etc are also common multiples of 12 and 10

- The
- The
**lowest common multiple**is the smallest common multiple between two numbers- This is useful when adding or subtracting fractions

- Write each number as a
**product of its prime factors** - Find the prime factors of the first number that are
**not**prime factors of the second number- Be careful with how many times a prime factor appears
- 12 = 2 × 2 × 3 and 10 = 2 × 5
- So 3 and
**one**of the 2s are not prime factors of the 10 - Equivalently 5 is not a prime factor of 12

- Be careful with how many times a prime factor appears
**Multiply**the first number by these extra prime factors- Either multiply 10 by 3 and 2
- Or multiply 12 by 5
- Both ways will give you the same answer

- Using a
**Venn diagram**can help- Put the common prime factors in the centre
- Put the other prime factors in the relevant circles
- The LCM is the product of
**all the numbers**in the**Venn diagram**

Find the highest common factor of 42 and 90.
Write as a product of prime factors

42 = 2 × 3 × 7 90 = 2 × 3 × 3 × 5

Write the prime factors in a Venn diagram if needed.

Multiply the common prime factors.

LCM = 7 × 2 × 3 × 3 × 5

This is the same as doing 42 × 3 × 5 or 90 × 7

**HCF = 630**

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