Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test 2025 - Free ALEKS Math Questions and Study Guide

Question: 1 / 400

What is the greatest common factor of 36 and 60?

6

8

12

To determine the greatest common factor (GCF) of 36 and 60, it's important to first find the prime factorization of each number.

The prime factorization of 36 is:

- 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2

The prime factorization of 60 is:

- 60 = 2 × 2 × 3 × 5 = 2^2 × 3 × 5

Next, to find the GCF, identify the lowest powers of all prime factors that are present in both factorizations.

For the number 2, the lowest power between 36 and 60 is 2^2.

For the number 3, the lowest power is 3^1.

The factor 5 appears only in the prime factorization of 60 and is not considered.

Now, multiply these together to find the GCF:

GCF = 2^2 × 3^1 = 4 × 3 = 12.

This shows that the greatest common factor of 36 and 60 is indeed 12. Hence, the correct answer reflects a proper understanding of prime factorization and the

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