What is the Greatest Common Factor of 31776 and 31782?

Greatest common factor (GCF) of 31776 and 31782 is 6.

GCF(31776,31782) = 6

We will now calculate the prime factors of 31776 and 31782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31776 and 31782.

How to find the GCF of 31776 and 31782?

We will first find the prime factorization of 31776 and 31782. After we will calculate the factors of 31776 and 31782 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31782

Prime factors of 31782 are 2, 3, 5297. Prime factorization of 31782 in exponential form is:

31782 = 2¹ × 3¹ × 5297¹

Step-3: Factors of 31776

List of positive integer factors of 31776 that divides 31776 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

Step-4: Factors of 31782

List of positive integer factors of 31782 that divides 31776 without a remainder.

1, 2, 3, 6, 5297, 10594, 15891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31776 and 31782. The biggest common factor number is the GCF number.
So the greatest common factor 31776 and 31782 is 6.

Also check out the Least Common Multiple of 31776 and 31782