Question

What factors dose 32 and 36 have in common

Answer 1

One way to approach this is to look at the difference between 32 and 36, which is 4. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Since both 32 and 36 are divisible by 4, the greatest common factor is 4. 
Another way to determine the greatest common factor is to find all the factors of the numbers and compare them. 
The factors of 32 are 1, 2, 4, 8, 16, and 32. 
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. 
The common factors are 1, 2, and 4. Therefore, the greatest common factor is 4. 

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. 
The prime factors of 32 are 2, 2, 2, 2, and 2. 
The prime factors of 36 are 2, 2, 3, and 3. 
The prime factors in common are 2 and 2, so the greatest common factor is 2 x 2 = 4.