What is the Greatest Common Factor of 196 and 213?

Greatest common factor (GCF) of 196 and 213 is 1.

GCF(196,213) = 1

We will now calculate the prime factors of 196 and 213, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 196 and 213.

How to find the GCF of 196 and 213?

We will first find the prime factorization of 196 and 213. After we will calculate the factors of 196 and 213 and find the biggest common factor number .

Step-1: Prime Factorization of 196

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

196 = 2² × 7²

Step-2: Prime Factorization of 213

Prime factors of 213 are 3, 71. Prime factorization of 213 in exponential form is:

213 = 3¹ × 71¹

Step-3: Factors of 196

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

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

Step-4: Factors of 213

List of positive integer factors of 213 that divides 196 without a remainder.

1, 3, 71

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 196 and 213. The biggest common factor number is the GCF number.
So the greatest common factor 196 and 213 is 1.

Also check out the Least Common Multiple of 196 and 213