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In the Common Core, factor pairs, multiples, and prime and composite numbers from 1 to 100 are grade 4 work. Start with the first ten multiples, which is counting up in the times tables. Then whether a number is a multiple, then factor pairs. Prime or composite comes last, because it rests on the factor pairs.

Factors and multiples

A factor divides a number exactly: 3 is a factor of 24, because 3 × 8 = 24. A multiple is a number times a whole number: 24 is a multiple of 3, and of 8, so a number is a multiple of each of its factors. To find every factor pair, start with 1 × 24 and go up: 2 × 12, 3 × 8, 4 × 6. The next would be 6 × 4, the same pair turned round, so stop there. A square number has a pair that is one number twice, 36 = 6 × 6, written once.

Prime or composite

A prime number has exactly two factors, 1 and itself, as 2, 3, 5, 7, 11 and 13. A composite number has more than two, as 9 = 3 × 3. The number 1 is neither, because it has only one factor. An odd number can still be composite: 51 = 3 × 17 and 91 = 7 × 13 look prime but are not.

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