What is the Greatest Common Factor of 31563 and 31575?

Greatest common factor (GCF) of 31563 and 31575 is 3.

GCF(31563,31575) = 3

We will now calculate the prime factors of 31563 and 31575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31563 and 31575.

How to find the GCF of 31563 and 31575?

We will first find the prime factorization of 31563 and 31575. After we will calculate the factors of 31563 and 31575 and find the biggest common factor number .

Step-1: Prime Factorization of 31563

Prime factors of 31563 are 3, 7, 167. Prime factorization of 31563 in exponential form is:

31563 = 3³ × 7¹ × 167¹

Step-2: Prime Factorization of 31575

Prime factors of 31575 are 3, 5, 421. Prime factorization of 31575 in exponential form is:

31575 = 3¹ × 5² × 421¹

Step-3: Factors of 31563

List of positive integer factors of 31563 that divides 31563 without a remainder.

1, 3, 7, 9, 21, 27, 63, 167, 189, 501, 1169, 1503, 3507, 4509, 10521

Step-4: Factors of 31575

List of positive integer factors of 31575 that divides 31563 without a remainder.

1, 3, 5, 15, 25, 75, 421, 1263, 2105, 6315, 10525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31563 and 31575. The biggest common factor number is the GCF number.
So the greatest common factor 31563 and 31575 is 3.

Also check out the Least Common Multiple of 31563 and 31575