Question

The greatest common factor of 114 and 190 is _____.

38
They are relatively prime.
19
2

Answer 1

To find the greatest common factor (GCF) of 114 and 190, we can start by determining the prime factorizations of both numbers.

1. **Prime factorization of 114:**
- 114 is even, so we start by dividing by 2:
\[
114 \div 2 = 57
\]
- Now factor 57:
\[
57 = 3 \times 19
\]
- Therefore, the prime factorization of 114 is:
\[
114 = 2 \times 3 \times 19
\]

2. **Prime factorization of 190:**
- 190 is also even, so we start by dividing by 2:
\[
190 \div 2 = 95
\]
- Now factor 95:
\[
95 = 5 \times 19
\]
- Therefore, the prime factorization of 190 is:
\[
190 = 2 \times 5 \times 19
\]

3. **Finding the GCF:**
- The common factors between 114 and 190 from their prime factorizations are 2 and 19.
- To find the GCF, we take the lowest power of all common prime factors:
- The common factors are 2 and 19.
- Therefore, the GCF is:
\[
GCF = 2 \times 19 = 38
\]

So the greatest common factor of 114 and 190 is **38**.