What is the Greatest Common Factor of 31764 and 31776?

Greatest common factor (GCF) of 31764 and 31776 is 12.

GCF(31764,31776) = 12

We will now calculate the prime factors of 31764 and 31776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31764 and 31776.

How to find the GCF of 31764 and 31776?

We will first find the prime factorization of 31764 and 31776. After we will calculate the factors of 31764 and 31776 and find the biggest common factor number .

Step-1: Prime Factorization of 31764

Prime factors of 31764 are 2, 3, 2647. Prime factorization of 31764 in exponential form is:

31764 = 2² × 3¹ × 2647¹

Step-2: Prime Factorization of 31776

Prime factors of 31776 are 2, 3, 331. Prime factorization of 31776 in exponential form is:

31776 = 2⁵ × 3¹ × 331¹

Step-3: Factors of 31764

List of positive integer factors of 31764 that divides 31764 without a remainder.

1, 2, 3, 4, 6, 12, 2647, 5294, 7941, 10588, 15882

Step-4: Factors of 31776

List of positive integer factors of 31776 that divides 31764 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 331, 662, 993, 1324, 1986, 2648, 3972, 5296, 7944, 10592, 15888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31764 and 31776. The biggest common factor number is the GCF number.
So the greatest common factor 31764 and 31776 is 12.

Also check out the Least Common Multiple of 31764 and 31776