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Factor strings are multiplication sentences. You can take any factor pair, put a multiplication symbol between them and you have a factor string. The longest factor string for any composite number is the prime factorization.

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210. And the longest factor string.

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Q: How do you find the factor string for a number?
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