Question

Find the greatest common factor (GCF).
28 and 50

Answer 1

To find the greatest common factor (GCF) of 28 and 50, we can start by finding the prime factorizations of each number.

**Prime Factorization:**

1. For 28:
- 28 is divisible by 2: \( 28 \div 2 = 14 \)
- 14 is divisible by 2: \( 14 \div 2 = 7 \)
- 7 is a prime number.

So, the prime factorization of 28 is:
\[
28 = 2^2 \times 7^1
\]

2. For 50:
- 50 is divisible by 2: \( 50 \div 2 = 25 \)
- 25 is divisible by 5: \( 25 \div 5 = 5 \)
- 5 is a prime number.

So, the prime factorization of 50 is:
\[
50 = 2^1 \times 5^2
\]

**Finding the GCF:**

Next, we identify the common prime factors and their lowest powers:

- The common prime factor between 28 and 50 is \( 2 \).
- The lowest power of \( 2 \) in their factorizations is \( 2^1 \).

Thus, the GCF of 28 and 50 is:
\[
GCF = 2^1 = 2
\]

Therefore, the greatest common factor (GCF) of 28 and 50 is **2**.