What is the Greatest Common Factor of 82671 and 82688?

Greatest common factor (GCF) of 82671 and 82688 is 17.

GCF(82671,82688) = 17

We will now calculate the prime factors of 82671 and 82688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82671 and 82688.

How to find the GCF of 82671 and 82688?

We will first find the prime factorization of 82671 and 82688. After we will calculate the factors of 82671 and 82688 and find the biggest common factor number .

Step-1: Prime Factorization of 82671

Prime factors of 82671 are 3, 17, 1621. Prime factorization of 82671 in exponential form is:

82671 = 3¹ × 17¹ × 1621¹

Step-2: Prime Factorization of 82688

Prime factors of 82688 are 2, 17, 19. Prime factorization of 82688 in exponential form is:

82688 = 2⁸ × 17¹ × 19¹

Step-3: Factors of 82671

List of positive integer factors of 82671 that divides 82671 without a remainder.

1, 3, 17, 51, 1621, 4863, 27557

Step-4: Factors of 82688

List of positive integer factors of 82688 that divides 82671 without a remainder.

1, 2, 4, 8, 16, 17, 19, 32, 34, 38, 64, 68, 76, 128, 136, 152, 256, 272, 304, 323, 544, 608, 646, 1088, 1216, 1292, 2176, 2432, 2584, 4352, 4864, 5168, 10336, 20672, 41344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82671 and 82688. The biggest common factor number is the GCF number.
So the greatest common factor 82671 and 82688 is 17.

Also check out the Least Common Multiple of 82671 and 82688