What is the Greatest Common Factor of 32640 and 32657?

Greatest common factor (GCF) of 32640 and 32657 is 17.

GCF(32640,32657) = 17

We will now calculate the prime factors of 32640 and 32657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32640 and 32657.

How to find the GCF of 32640 and 32657?

We will first find the prime factorization of 32640 and 32657. After we will calculate the factors of 32640 and 32657 and find the biggest common factor number .

Step-1: Prime Factorization of 32640

Prime factors of 32640 are 2, 3, 5, 17. Prime factorization of 32640 in exponential form is:

32640 = 2⁷ × 3¹ × 5¹ × 17¹

Step-2: Prime Factorization of 32657

Prime factors of 32657 are 17, 113. Prime factorization of 32657 in exponential form is:

32657 = 17² × 113¹

Step-3: Factors of 32640

List of positive integer factors of 32640 that divides 32640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 272, 320, 340, 384, 408, 480, 510, 544, 640, 680, 816, 960, 1020, 1088, 1360, 1632, 1920, 2040, 2176, 2720, 3264, 4080, 5440, 6528, 8160, 10880, 16320

Step-4: Factors of 32657

List of positive integer factors of 32657 that divides 32640 without a remainder.

1, 17, 113, 289, 1921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32640 and 32657. The biggest common factor number is the GCF number.
So the greatest common factor 32640 and 32657 is 17.

Also check out the Least Common Multiple of 32640 and 32657