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Factors and Multiples

1. Multiples

Multiples of a number can be divided exactly by that number with no reminder.

Example:

Multiples of 3: 3,6,9,12,15……..

Multiples of 8: 8,16,24,32……..

2. Factors

Factors of a number are whole numbers that divide into the number exactly.

Example: Factors of 12 are 1,2,3,4,6,and 12

3. Common Factors

The common factors of two numbers are the factors that the numbers have in common.

Example:

Factors of 12: 1,2,3,4,6,12

Factors of 15: 1,3,5,15

Therefore common factors of 12 and 15 are 1 and 3

4. Prime Factorisation

The process of expressing a composite number as the product of prime factors is called prime factorisation.

Example

30 = 2x3x5

2,3, and 5 are the prime factors of 30

5. Highest Common Factor (H.C.F.)

The largest of the common factors is called the highest common factor.

6. Lowest Common Factor (L.C.M)

The smallest of the common multiples is called the lowest common multiple

Example

18 = 2x3x3 = 2×3^2

60 = 2x2x3x5 = 2^2x3x5

H.C.F. = 2×3 = 6

L.C.M. = 2^2 x 3^2 x 5 = 180

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