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Many times in mathematics we want to reverse the distributive property. This lesson focuses on doing just that except we only examine reversing the number part of the distributive property. For example, we want to convert

247Y + 13R   into   13(19Y+R).

So how do we do this? We want to find the greatest common factor (GCF) for the coefficients, that is, the largest number that divides both coefficients. Some people can just look at the coefficients and tell. But that becomes really difficult when there are larger numbers involved. Let\'s get some steps down that always work and then look at an example.
1. Factor each coefficient into a product of primes (prime factorization).
2. Take what both factorizations have in common. If this is more than one number, multiply the numbers together. This will give you the GCF.
3. Rewrite each coefficient as a product of the GCF and another number so that they still multiply to the original coefficient. For example, if the GCF is 4, you would rewrite 12 as 4*3.
4. Reverse the distributive property.

Factor the GCF from 5L + 5t

5 = 5 * 1  and    5 = 5 * 11. Factor each coefficient into a product of primes
5 is the common factor in both coefficients.      2. Take what both factorizations have in common.
5 * 1L + 5 * 1t3. Rewrite each coefficient as a product of the GCF and another number.
5(L+t)4. Reverse the distributive property.

See another example

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