Multiples and factors - EdexcelHighest common factor and lowest common multiple
Prime numbers, factors and multiples are essential building blocks for a lot of number work. Knowledge of how to use these numbers will improve arithmetic and make calculations more efficient.
A common factor is a factorA factor is a number which divides exactly into another number. 1 is a factor of every number and every number is a factor of itself. A number can have several factors. Example: 1, 2, 5 and 10 are the factors of 10. that is shared by two or more numbers. For example, a common factor of 8 and 10 is 2, as 2 is a factor of 8, and 2 is also a factor of 10.
The highest common factor (HCF)The highest common factor (HCF) of two numbers is the largest number which will divide exactly into both of them, for example, the highest common factor of 24 and 36 is 12. is found by finding all common factors of two numbers and selecting the largest one.
For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.
Question
Find the highest common factor of 9 and 21.
Start by listing the factors of 9 and 21:
factors of 9: 1, 3, 9
factors of 21: 1, 3, 7, 21
The common factors of 9 and 21 are 1 and 3, so the highest common factor of 9 and 21 is 3.
Lowest common multiple
A common multiple is a number that is a shared multipleThe multiple of a number is the number multiplied by an integer. The first four multiples of 5 are 5, 10, 15 and 20. of two or more numbers. For example, 24 is a common multiple of 8 and 12, as 24 is in the 8 times tables (\(8 \times 3 = 24\)) and 24 is in the 12 times tables (\(12 \times 2 = 24\)).
The lowest common multiple (LCM)The smallest positive number that is a multiple of two or more numbers. is found by listing the multiples of each number and circling any common multiples. The lowest one is the lowest common multiple.
Question
Find the lowest common multiple of 5 and 6.
List the multiples of 5 and 6:
multiples of 5: 5, 10, 15, 20, 25, 30, 35...
multiples of 6: 6, 12, 18, 24, 30...
The lowest common multiple of 5 and 6 is 30, as it is the first multiple found in both lists.