Question

What is the greatest common factor of 79 and 42?

Answer 1

To determine the greatest common factor (GCF) of 79 and 42, we can use the method of identifying the factors of each number or using the Euclidean algorithm.

1. **Factors Method**:
- The factors of 79 are: 1 and 79 (since 79 is a prime number).
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.

The only common factor between 79 and 42 is 1.

2. **Euclidean Algorithm**:
- We start with the two numbers: 79 and 42.
- We perform the division:
- \( 79 \div 42 = 1 \) with a remainder of \( 79 - 42 = 37 \).
- Next, we take the previous divisor (42) and the remainder (37):
- \( 42 \div 37 = 1 \) with a remainder of \( 42 - 37 = 5 \).
- We repeat this with the new divisor (37) and the new remainder (5):
- \( 37 \div 5 = 7 \) with a remainder of \( 37 - 35 = 2 \).
- Continuing, we take 5 and 2:
- \( 5 \div 2 = 2 \) with a remainder of \( 5 - 4 = 1 \).
- Finally, we take 2 and 1:
- \( 2 \div 1 = 2 \) with a remainder of \( 2 - 2 = 0 \).

When the remainder reaches 0, the last non-zero remainder is the GCF.

Thus, the GCF of 79 and 42 is:

\[
\boxed{1}
\]