The greatest common factor of 114 and 190 is _____.

Question

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.