What is the Greatest Common Factor of 190 and 210?

Greatest common factor (GCF) of 190 and 210 is 10.

GCF(190,210) = 10

We will now calculate the prime factors of 190 and 210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 190 and 210.

How to find the GCF of 190 and 210?

We will first find the prime factorization of 190 and 210. After we will calculate the factors of 190 and 210 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 210

Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:

210 = 2¹ × 3¹ × 5¹ × 7¹

Step-3: Factors of 190

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

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

Step-4: Factors of 210

List of positive integer factors of 210 that divides 190 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 190 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 190 and 210 is 10.

Also check out the Least Common Multiple of 190 and 210