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greatest common factor of 11 and 33

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2 Answers

Factors are numbers you multiply together to get another number. 

The factors of 11 are: 1 and 11

The factors of 33 are: 1, 3, 11, and 33 (because 1x33= 33, and 3x11=33)

Therefore, the greatest common factor is the largest factor that both numbers have in common and in this case the greatest common factor is 11. 

If the smaller number is the factor of the larger number, like with your case of 11 and 33 (33=3*11), then the answer is the smaller of the two numbers, in this case 11.

Otherwise there is an easy method, which I will show here with 64 and 40 as an example:


= GCF(52,12) because 64 - 1*52 = 12

= GCF(12,4) because 52 - 4*12 = 4

= 4 because of the above rule since 12 = 3*4.

This procedure is called Euclid's Algorithm and has the advantage of not requiring factoring the two integers. Factoring gets hard when the integers are very large. For large pairs of integers, it is the fastest method possible.