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The simplest factor chains are the factor pairs of a given number written out as multiplication sentences. Example: 36

36 x 1, 18 x 2, 12 x 3, 9 x 4

To make longer factor chains, factor any of the above that have a composite number.

2 x 2 x 9, 2 x 3 x 6

Repeat the process. When all the factors are prime, the longest factor string will be the prime factorization.

2 x 2 x 3 x 3

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Q: How do you work out factor chains?
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