What is the Greatest Common Factor of 31784 and 31792?

Greatest common factor (GCF) of 31784 and 31792 is 8.

GCF(31784,31792) = 8

We will now calculate the prime factors of 31784 and 31792, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31784 and 31792.

How to find the GCF of 31784 and 31792?

We will first find the prime factorization of 31784 and 31792. After we will calculate the factors of 31784 and 31792 and find the biggest common factor number .

Step-1: Prime Factorization of 31784

Prime factors of 31784 are 2, 29, 137. Prime factorization of 31784 in exponential form is:

31784 = 2³ × 29¹ × 137¹

Step-2: Prime Factorization of 31792

Prime factors of 31792 are 2, 1987. Prime factorization of 31792 in exponential form is:

31792 = 2⁴ × 1987¹

Step-3: Factors of 31784

List of positive integer factors of 31784 that divides 31784 without a remainder.

1, 2, 4, 8, 29, 58, 116, 137, 232, 274, 548, 1096, 3973, 7946, 15892

Step-4: Factors of 31792

List of positive integer factors of 31792 that divides 31784 without a remainder.

1, 2, 4, 8, 16, 1987, 3974, 7948, 15896

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31784 and 31792. The biggest common factor number is the GCF number.
So the greatest common factor 31784 and 31792 is 8.

Also check out the Least Common Multiple of 31784 and 31792