FTCE General Knowledge Math Practice Test

What is the greatest common factor (GCF) of the numbers 12, 20, and 36?

1. 12

2. 6

3. 4

4. 2

The correct answer is: 4

To find the greatest common factor (GCF) of the numbers 12, 20, and 36, we start by determining the prime factorization of each number: - The prime factors of 12 are \(2^2 \times 3\) (which comes from \(2 \times 2 \times 3\)). - The prime factors of 20 are \(2^2 \times 5\) (which comes from \(2 \times 2 \times 5\)). - The prime factors of 36 are \(2^2 \times 3^2\) (which comes from \(2 \times 2 \times 3 \times 3\)). Next, we identify the common prime factors among all three numbers. The only prime factor they share is \(2\), and the lowest power of \(2\) present in all factorizations is \(2^2\). Now we can calculate the GCF by taking the lowest powers of all common prime factors: - For \(2\), the lowest power is \(2^2\), which equals 4. Therefore, the GCF of 12, 20, and 36 is 4. This