What is the Greatest Common Factor of 31524 and 31536?

Greatest common factor (GCF) of 31524 and 31536 is 12.

GCF(31524,31536) = 12

We will now calculate the prime factors of 31524 and 31536, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31524 and 31536.

How to find the GCF of 31524 and 31536?

We will first find the prime factorization of 31524 and 31536. After we will calculate the factors of 31524 and 31536 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 31536

Prime factors of 31536 are 2, 3, 73. Prime factorization of 31536 in exponential form is:

31536 = 2⁴ × 3³ × 73¹

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 31536

List of positive integer factors of 31536 that divides 31524 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 73, 108, 144, 146, 216, 219, 292, 432, 438, 584, 657, 876, 1168, 1314, 1752, 1971, 2628, 3504, 3942, 5256, 7884, 10512, 15768

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31524 and 31536. The biggest common factor number is the GCF number.
So the greatest common factor 31524 and 31536 is 12.

Also check out the Least Common Multiple of 31524 and 31536