What is the Greatest Common Factor of 175 and 190?

Greatest common factor (GCF) of 175 and 190 is 5.

GCF(175,190) = 5

We will now calculate the prime factors of 175 and 190, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 175 and 190.

How to find the GCF of 175 and 190?

We will first find the prime factorization of 175 and 190. After we will calculate the factors of 175 and 190 and find the biggest common factor number .

Step-1: Prime Factorization of 175

Prime factors of 175 are 5, 7. Prime factorization of 175 in exponential form is:

175 = 5² × 7¹

Step-2: Prime Factorization of 190

Prime factors of 190 are 2, 5, 19. Prime factorization of 190 in exponential form is:

190 = 2¹ × 5¹ × 19¹

Step-3: Factors of 175

List of positive integer factors of 175 that divides 175 without a remainder.

1, 5, 7, 25, 35

Step-4: Factors of 190

List of positive integer factors of 190 that divides 175 without a remainder.

1, 2, 5, 10, 19, 38, 95

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 175 and 190. The biggest common factor number is the GCF number.
So the greatest common factor 175 and 190 is 5.

Also check out the Least Common Multiple of 175 and 190