What is the Greatest Common Factor of 51590 and 51600?

Greatest common factor (GCF) of 51590 and 51600 is 10.

GCF(51590,51600) = 10

We will now calculate the prime factors of 51590 and 51600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51590 and 51600.

How to find the GCF of 51590 and 51600?

We will first find the prime factorization of 51590 and 51600. After we will calculate the factors of 51590 and 51600 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 51600

Prime factors of 51600 are 2, 3, 5, 43. Prime factorization of 51600 in exponential form is:

51600 = 2⁴ × 3¹ × 5² × 43¹

Step-3: Factors of 51590

List of positive integer factors of 51590 that divides 51590 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

Step-4: Factors of 51600

List of positive integer factors of 51600 that divides 51590 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 43, 48, 50, 60, 75, 80, 86, 100, 120, 129, 150, 172, 200, 215, 240, 258, 300, 344, 400, 430, 516, 600, 645, 688, 860, 1032, 1075, 1200, 1290, 1720, 2064, 2150, 2580, 3225, 3440, 4300, 5160, 6450, 8600, 10320, 12900, 17200, 25800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51590 and 51600. The biggest common factor number is the GCF number.
So the greatest common factor 51590 and 51600 is 10.

Also check out the Least Common Multiple of 51590 and 51600