Factor Pairs and Multiplication

Factors come in pairs because they come from multiplication statements. For example, the multiplication statement:

2 × 5 = 10

says that the factors 2 and 5, result in a product of 10:

2 is a factor of 10
5 is a factor of 10

and also:
10 is a multiple of 2
10 is a multiple of 5

Of course, the two factors in a multiplication can be the same. For example:

3 × 3 = 9

so 3 is a factor of 9 and 9 is a multiple of 3.

To find all the factors of a number, find every multiplication with that product. For example, to find all the factors of 10:

 1 × 10 = 10 So 1 and 10 are factors of 10 2 × 5 = 10 So 2 and 5 are factors of 10 3 × ? = 10 10 is not a multiple of 3, 3 is not a factor of 10 4 × ? = 10 10 is not a multiple of 4, 4 is not a factor of 10 5 × ... We can stop with 4. Why? Because we've already found 5 as a factor. Any more factors we find will be repeats - the same pair of numbers, but reversed. For 5 × 2 = 10, the factor pair is 5 and 2, but we've already found the pair 2 and 5.

So the factors of 10 are: 1, 2, 5, 10

Write the possible multiplication statements in order so that you don't miss any factors and you can tell when the factor pairs start repeating.

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Factor Pairs and Multiplication

Write every multiplication statement that has the number as a product, until the factor pairs begin to repeat.

Then write all the factors of the number.

 Find all the factors of 16. Find all the factors of 78.