What is the Greatest Common Factor of 31648 and 31664?

Greatest common factor (GCF) of 31648 and 31664 is 16.

GCF(31648,31664) = 16

We will now calculate the prime factors of 31648 and 31664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31648 and 31664.

How to find the GCF of 31648 and 31664?

We will first find the prime factorization of 31648 and 31664. After we will calculate the factors of 31648 and 31664 and find the biggest common factor number .

Step-1: Prime Factorization of 31648

Prime factors of 31648 are 2, 23, 43. Prime factorization of 31648 in exponential form is:

31648 = 2⁵ × 23¹ × 43¹

Step-2: Prime Factorization of 31664

Prime factors of 31664 are 2, 1979. Prime factorization of 31664 in exponential form is:

31664 = 2⁴ × 1979¹

Step-3: Factors of 31648

List of positive integer factors of 31648 that divides 31648 without a remainder.

1, 2, 4, 8, 16, 23, 32, 43, 46, 86, 92, 172, 184, 344, 368, 688, 736, 989, 1376, 1978, 3956, 7912, 15824

Step-4: Factors of 31664

List of positive integer factors of 31664 that divides 31648 without a remainder.

1, 2, 4, 8, 16, 1979, 3958, 7916, 15832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31648 and 31664. The biggest common factor number is the GCF number.
So the greatest common factor 31648 and 31664 is 16.

Also check out the Least Common Multiple of 31648 and 31664