How Many Factors?

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The video above is from "Let's Do Math"

Here is a different way to calculate the number of factors a number has. It appeared in Mathematical Pie, a Mathematical Association publication.

The prime factorisation of 600 is 2³ x 5² x 3. We can make all the factors of 600 by choosing from four possibilities for the 2 (to include it 0, 1, 2 or 3 times); three possibilities for the 5 (to include it 0, I or 2 times) and two possibilities for the 3 (to include it or not).

Altogether 4 x 3 x 2 = 24 possibilities (if we don't choose any of the three this will give the factor l). So 600 has 24 factors.

When you know the number of factors of a number it is also helpful to know that the factors come in pairs. For example the factors of 96, shown in their pairs, are:

1 x 96
2 x 48
3 x 32
4 x 24
6 x 16
8 x 12

Square numbers have an odd number of factors. One factor, the square root, is multiplied by itself to give the number. For example the factors of 36 are:

1 x 36
2 x 18
3 x 12
4 x 9
6²

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How Many Factors?

Work out the number of factors a number has then write them all as a list.

Factor Trees Factor Pairs Level 1 Level 2 Level 3 Level 4 Menu Help More...

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