Final answer:
The greatest common factor of 64 and 36 is 4. After dividing each number by the GCF, the sum of 100 can be rewritten as the product of 4 and the sum of the co-factors, which is 25. Thus, 100 can be expressed as 4 x 25.
Step-by-step explanation:
The student is asking for the greatest common factor (GCF) of the numbers 64 and 36, and to rewrite the sum 100 as a product of the GCF and another factor. To find the GCF, you list the factors of both numbers and find the largest one they have in common.
Factors of 64 are 1, 2, 4, 8, 16, 32, 64. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCF of 64 and 36 is 4.
So we divide both numbers by the GCF to find the co-factors:
- 64 divided by 4 is 16.
- 36 divided by 4 is 9.
We can now rewrite the sum as follows:
100 = (GCF) x (Sum of co-factors)
100 = 4 x (16 + 9)
100 = 4 x 25