What is the Greatest Common Factor of 31520 and 31536?

Greatest common factor (GCF) of 31520 and 31536 is 16.

GCF(31520,31536) = 16

We will now calculate the prime factors of 31520 and 31536, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31520 and 31536.

How to find the GCF of 31520 and 31536?

We will first find the prime factorization of 31520 and 31536. After we will calculate the factors of 31520 and 31536 and find the biggest common factor number .

Step-1: Prime Factorization of 31520

Prime factors of 31520 are 2, 5, 197. Prime factorization of 31520 in exponential form is:

31520 = 2⁵ × 5¹ × 197¹

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 31520

List of positive integer factors of 31520 that divides 31520 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 197, 394, 788, 985, 1576, 1970, 3152, 3940, 6304, 7880, 15760

Step-4: Factors of 31536

List of positive integer factors of 31536 that divides 31520 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 31520 and 31536. The biggest common factor number is the GCF number.
So the greatest common factor 31520 and 31536 is 16.

Also check out the Least Common Multiple of 31520 and 31536