What is the Greatest Common Factor of 315 and 322?

Greatest common factor (GCF) of 315 and 322 is 7.

GCF(315,322) = 7

We will now calculate the prime factors of 315 and 322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 315 and 322.

How to find the GCF of 315 and 322?

We will first find the prime factorization of 315 and 322. After we will calculate the factors of 315 and 322 and find the biggest common factor number .

Step-1: Prime Factorization of 315

Prime factors of 315 are 3, 5, 7. Prime factorization of 315 in exponential form is:

315 = 3² × 5¹ × 7¹

Step-2: Prime Factorization of 322

Prime factors of 322 are 2, 7, 23. Prime factorization of 322 in exponential form is:

322 = 2¹ × 7¹ × 23¹

Step-3: Factors of 315

List of positive integer factors of 315 that divides 315 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105

Step-4: Factors of 322

List of positive integer factors of 322 that divides 315 without a remainder.

1, 2, 7, 14, 23, 46, 161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 315 and 322. The biggest common factor number is the GCF number.
So the greatest common factor 315 and 322 is 7.

Also check out the Least Common Multiple of 315 and 322