What is the Greatest Common Factor of 31269 and 31275?

Greatest common factor (GCF) of 31269 and 31275 is 3.

GCF(31269,31275) = 3

We will now calculate the prime factors of 31269 and 31275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31269 and 31275.

How to find the GCF of 31269 and 31275?

We will first find the prime factorization of 31269 and 31275. After we will calculate the factors of 31269 and 31275 and find the biggest common factor number .

Step-1: Prime Factorization of 31269

Prime factors of 31269 are 3, 7, 1489. Prime factorization of 31269 in exponential form is:

31269 = 3¹ × 7¹ × 1489¹

Step-2: Prime Factorization of 31275

Prime factors of 31275 are 3, 5, 139. Prime factorization of 31275 in exponential form is:

31275 = 3² × 5² × 139¹

Step-3: Factors of 31269

List of positive integer factors of 31269 that divides 31269 without a remainder.

1, 3, 7, 21, 1489, 4467, 10423

Step-4: Factors of 31275

List of positive integer factors of 31275 that divides 31269 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 139, 225, 417, 695, 1251, 2085, 3475, 6255, 10425

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31269 and 31275. The biggest common factor number is the GCF number.
So the greatest common factor 31269 and 31275 is 3.

Also check out the Least Common Multiple of 31269 and 31275