What is the Greatest Common Factor of 31506 and 31514?

Greatest common factor (GCF) of 31506 and 31514 is 2.

GCF(31506,31514) = 2

We will now calculate the prime factors of 31506 and 31514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31506 and 31514.

How to find the GCF of 31506 and 31514?

We will first find the prime factorization of 31506 and 31514. After we will calculate the factors of 31506 and 31514 and find the biggest common factor number .

Step-1: Prime Factorization of 31506

Prime factors of 31506 are 2, 3, 59, 89. Prime factorization of 31506 in exponential form is:

31506 = 2¹ × 3¹ × 59¹ × 89¹

Step-2: Prime Factorization of 31514

Prime factors of 31514 are 2, 7, 2251. Prime factorization of 31514 in exponential form is:

31514 = 2¹ × 7¹ × 2251¹

Step-3: Factors of 31506

List of positive integer factors of 31506 that divides 31506 without a remainder.

1, 2, 3, 6, 59, 89, 118, 177, 178, 267, 354, 534, 5251, 10502, 15753

Step-4: Factors of 31514

List of positive integer factors of 31514 that divides 31506 without a remainder.

1, 2, 7, 14, 2251, 4502, 15757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31506 and 31514. The biggest common factor number is the GCF number.
So the greatest common factor 31506 and 31514 is 2.

Also check out the Least Common Multiple of 31506 and 31514