Workkeys Math Practice Test

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What is the greatest common factor of 24 and 36?

To find the greatest common factor (GCF) of two numbers, we first determine the prime factorization of each number.

For 24, the prime factorization is:

24 = 2 × 2 × 2 × 3, or in exponential form, 2^3 × 3^1.

For 36, the prime factorization is:

36 = 2 × 2 × 3 × 3, or in exponential form, 2^2 × 3^2.

Next, we identify the common prime factors. The common prime factors between 24 and 36 are 2 and 3.

To find the GCF, we take the lowest power of each common prime factor:

- For the factor 2, the lowest power is 2^2 (from 36).

- For the factor 3, the lowest power is 3^1 (from 24).

Now, we calculate the GCF by multiplying these together:

GCF = 2^2 × 3^1 = 4 × 3 = 12.

Thus, the greatest common factor of 24 and 36 is 12. This value is correct because it is the largest number that can

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