What is the Greatest Common Factor of 252 and 262?

Greatest common factor (GCF) of 252 and 262 is 2.

GCF(252,262) = 2

We will now calculate the prime factors of 252 and 262, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 252 and 262.

How to find the GCF of 252 and 262?

We will first find the prime factorization of 252 and 262. After we will calculate the factors of 252 and 262 and find the biggest common factor number .

Step-1: Prime Factorization of 252

Prime factors of 252 are 2, 3, 7. Prime factorization of 252 in exponential form is:

252 = 2² × 3² × 7¹

Step-2: Prime Factorization of 262

Prime factors of 262 are 2, 131. Prime factorization of 262 in exponential form is:

262 = 2¹ × 131¹

Step-3: Factors of 252

List of positive integer factors of 252 that divides 252 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126

Step-4: Factors of 262

List of positive integer factors of 262 that divides 252 without a remainder.

1, 2, 131

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 252 and 262. The biggest common factor number is the GCF number.
So the greatest common factor 252 and 262 is 2.

Also check out the Least Common Multiple of 252 and 262