What is the Greatest Common Factor of 31536 and 31552?

Greatest common factor (GCF) of 31536 and 31552 is 16.

GCF(31536,31552) = 16

We will now calculate the prime factors of 31536 and 31552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31536 and 31552.

How to find the GCF of 31536 and 31552?

We will first find the prime factorization of 31536 and 31552. After we will calculate the factors of 31536 and 31552 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31552

Prime factors of 31552 are 2, 17, 29. Prime factorization of 31552 in exponential form is:

31552 = 2⁶ × 17¹ × 29¹

Step-3: Factors of 31536

List of positive integer factors of 31536 that divides 31536 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

Step-4: Factors of 31552

List of positive integer factors of 31552 that divides 31536 without a remainder.

1, 2, 4, 8, 16, 17, 29, 32, 34, 58, 64, 68, 116, 136, 232, 272, 464, 493, 544, 928, 986, 1088, 1856, 1972, 3944, 7888, 15776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31536 and 31552. The biggest common factor number is the GCF number.
So the greatest common factor 31536 and 31552 is 16.

Also check out the Least Common Multiple of 31536 and 31552