What is the Greatest Common Factor of 51584 and 51590?

Greatest common factor (GCF) of 51584 and 51590 is 2.

GCF(51584,51590) = 2

We will now calculate the prime factors of 51584 and 51590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51584 and 51590.

How to find the GCF of 51584 and 51590?

We will first find the prime factorization of 51584 and 51590. After we will calculate the factors of 51584 and 51590 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 51590

Prime factors of 51590 are 2, 5, 7, 11, 67. Prime factorization of 51590 in exponential form is:

51590 = 2¹ × 5¹ × 7¹ × 11¹ × 67¹

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 51590

List of positive integer factors of 51590 that divides 51584 without a remainder.

1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 67, 70, 77, 110, 134, 154, 335, 385, 469, 670, 737, 770, 938, 1474, 2345, 3685, 4690, 5159, 7370, 10318, 25795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51584 and 51590. The biggest common factor number is the GCF number.
So the greatest common factor 51584 and 51590 is 2.

Also check out the Least Common Multiple of 51584 and 51590