What is the Greatest Common Factor of 51600 and 51612?

Greatest common factor (GCF) of 51600 and 51612 is 12.

GCF(51600,51612) = 12

We will now calculate the prime factors of 51600 and 51612, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51600 and 51612.

How to find the GCF of 51600 and 51612?

We will first find the prime factorization of 51600 and 51612. After we will calculate the factors of 51600 and 51612 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 51612

Prime factors of 51612 are 2, 3, 11, 17, 23. Prime factorization of 51612 in exponential form is:

51612 = 2² × 3¹ × 11¹ × 17¹ × 23¹

Step-3: Factors of 51600

List of positive integer factors of 51600 that divides 51600 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

Step-4: Factors of 51612

List of positive integer factors of 51612 that divides 51600 without a remainder.

1, 2, 3, 4, 6, 11, 12, 17, 22, 23, 33, 34, 44, 46, 51, 66, 68, 69, 92, 102, 132, 138, 187, 204, 253, 276, 374, 391, 506, 561, 748, 759, 782, 1012, 1122, 1173, 1518, 1564, 2244, 2346, 3036, 4301, 4692, 8602, 12903, 17204, 25806

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51600 and 51612. The biggest common factor number is the GCF number.
So the greatest common factor 51600 and 51612 is 12.

Also check out the Least Common Multiple of 51600 and 51612