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## Topic 5: Multiples, Factors and Primes

The multiples of an integer are the numbers in its times-table.

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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.

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

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Factors come in pairs:

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The factors of 10 are 1, 10, 2 and 5

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

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

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

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The factors of 15 are 1, 15, 3, and 5

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

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

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

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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.

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

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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.

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Note that 1 is a common factor for all integers.

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