What is the Greatest Common Factor of 189 and 196?

Greatest common factor (GCF) of 189 and 196 is 7.

GCF(189,196) = 7

We will now calculate the prime factors of 189 and 196, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 189 and 196.

How to find the GCF of 189 and 196?

We will first find the prime factorization of 189 and 196. After we will calculate the factors of 189 and 196 and find the biggest common factor number .

Step-1: Prime Factorization of 189

Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:

189 = 3³ × 7¹

Step-2: Prime Factorization of 196

Prime factors of 196 are 2, 7. Prime factorization of 196 in exponential form is:

196 = 2² × 7²

Step-3: Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63

Step-4: Factors of 196

List of positive integer factors of 196 that divides 189 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 189 and 196. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 196 is 7.

Also check out the Least Common Multiple of 189 and 196