What is the Greatest Common Factor of 51584 and 51597?

Greatest common factor (GCF) of 51584 and 51597 is 13.

GCF(51584,51597) = 13

We will now calculate the prime factors of 51584 and 51597, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51584 and 51597.

How to find the GCF of 51584 and 51597?

We will first find the prime factorization of 51584 and 51597. After we will calculate the factors of 51584 and 51597 and find the biggest common factor number .

Step-1: Prime Factorization of 51584

Prime factors of 51584 are 2, 13, 31. Prime factorization of 51584 in exponential form is:

51584 = 2⁷ × 13¹ × 31¹

Step-2: Prime Factorization of 51597

Prime factors of 51597 are 3, 7, 13. Prime factorization of 51597 in exponential form is:

51597 = 3⁴ × 7² × 13¹

Step-3: Factors of 51584

List of positive integer factors of 51584 that divides 51584 without a remainder.

1, 2, 4, 8, 13, 16, 26, 31, 32, 52, 62, 64, 104, 124, 128, 208, 248, 403, 416, 496, 806, 832, 992, 1612, 1664, 1984, 3224, 3968, 6448, 12896, 25792

Step-4: Factors of 51597

List of positive integer factors of 51597 that divides 51584 without a remainder.

1, 3, 7, 9, 13, 21, 27, 39, 49, 63, 81, 91, 117, 147, 189, 273, 351, 441, 567, 637, 819, 1053, 1323, 1911, 2457, 3969, 5733, 7371, 17199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51584 and 51597. The biggest common factor number is the GCF number.
So the greatest common factor 51584 and 51597 is 13.

Also check out the Least Common Multiple of 51584 and 51597