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## Topic 5: Multiples, Factors and Primes    The multiples of an integer are the numbers in its times-table.

So, the multiples of 2 are 2, 4, 6, 8, 10, and so on.

The multiples of 3 are 3, 6, 9, 12, 15, and so on.

The multiples of 10 are 10, 20, 30, 40, 50, and so on.

The factors of an integer are the integers that it will divide by, leaving no remainder.

Factors come in pairs:

The factors of 10 are 1, 10, 2 and 5

(because 1 × 10 = 10, and 2 × 5 = 10).

The factors of 12 are 1, 12, 2, 6, 3 and 4

(because 1 × 12 = 12, and 2 × 6 = 12 and 3 × 4 = 12).

The factors of 15 are 1, 15, 3, and 5

(because 1 × 15 = 15, and 3 × 5 = 15).

Every integer has at least 2 factors: 1, and the integer itself.

A prime number is an integer that has two factors: 1, and the integer itself.

2 is a prime number because its only factors are 1 and 2.

3 is a prime number because its only factors are 1 and 3.

5 is a prime number because its only factors are 1 and 5.

7 is a prime number because its only factors are 1 and 7.

Note that 1 is not considered a prime number. It has only one factor (itself). The first prime number is 2.

Any factors that two integers share in common are called common factors.

The only common factor of 2 and 5 is 1.

The common factors of 6 and 9 are 1 and 3.

The common factors of 4 and 8 are 1, 2 and 4.

The common factors of 20 and 30 are 1, 2, 5, and 10.

The common factors of 24 and 30 are 1, 2, 3, 4, and 6.

Note that 1 is a common factor for all integers.

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