Find the greatest common factor of the two numbers 20 + 36

Rewrite the sum from above using the distributive property.

The greatest common factor is 4.

Step-by-step explanation:

I'm going to do this the way you requested it. Then I'll do it another way which is better for larger numbers.

The highest common factor that will go into both these numbers is 4.

S = 20 + 36

S = 4 (5 + 6) There is nothing common between 5 and 6. 5 is a prime. It does not divide down further.

This may look like something that is easy to do until you have some really huge numbers that have lots in common like 480 and 800. Then the best way to do it is factor it into prime factors.

800: 2 * 2 * 2 * 2 * 2 * 5 * 5

480: 2 * 2 * 2 * 2 * 2 * 3 * 5

The common factor is bolded 2^5 * 5

2^5 = 32

32 * 5 = 160

The highest common Factor is 160

Conclusion

For small numbers, like 20 and 36, use the distributive property. It can be used even for larger numbers, but you have to be able to do the factoring in your head, or it's easier if you can.

For larger numbers I would do prime factors which is a whole different question.