What is the Greatest Common Factor of 31664 and 31672?

Greatest common factor (GCF) of 31664 and 31672 is 8.

GCF(31664,31672) = 8

We will now calculate the prime factors of 31664 and 31672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31664 and 31672.

How to find the GCF of 31664 and 31672?

We will first find the prime factorization of 31664 and 31672. After we will calculate the factors of 31664 and 31672 and find the biggest common factor number .

Step-1: Prime Factorization of 31664

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

31664 = 2⁴ × 1979¹

Step-2: Prime Factorization of 31672

Prime factors of 31672 are 2, 37, 107. Prime factorization of 31672 in exponential form is:

31672 = 2³ × 37¹ × 107¹

Step-3: Factors of 31664

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

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

Step-4: Factors of 31672

List of positive integer factors of 31672 that divides 31664 without a remainder.

1, 2, 4, 8, 37, 74, 107, 148, 214, 296, 428, 856, 3959, 7918, 15836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31664 and 31672. The biggest common factor number is the GCF number.
So the greatest common factor 31664 and 31672 is 8.

Also check out the Least Common Multiple of 31664 and 31672