What is the Greatest Common Factor of 31524 and 31538?

Greatest common factor (GCF) of 31524 and 31538 is 2.

GCF(31524,31538) = 2

We will now calculate the prime factors of 31524 and 31538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31524 and 31538.

How to find the GCF of 31524 and 31538?

We will first find the prime factorization of 31524 and 31538. After we will calculate the factors of 31524 and 31538 and find the biggest common factor number .

Step-1: Prime Factorization of 31524

Prime factors of 31524 are 2, 3, 37, 71. Prime factorization of 31524 in exponential form is:

31524 = 2² × 3¹ × 37¹ × 71¹

Step-2: Prime Factorization of 31538

Prime factors of 31538 are 2, 13, 1213. Prime factorization of 31538 in exponential form is:

31538 = 2¹ × 13¹ × 1213¹

Step-3: Factors of 31524

List of positive integer factors of 31524 that divides 31524 without a remainder.

1, 2, 3, 4, 6, 12, 37, 71, 74, 111, 142, 148, 213, 222, 284, 426, 444, 852, 2627, 5254, 7881, 10508, 15762

Step-4: Factors of 31538

List of positive integer factors of 31538 that divides 31524 without a remainder.

1, 2, 13, 26, 1213, 2426, 15769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31524 and 31538. The biggest common factor number is the GCF number.
So the greatest common factor 31524 and 31538 is 2.

Also check out the Least Common Multiple of 31524 and 31538