What is the Greatest Common Factor of 51675 and 51680?

Greatest common factor (GCF) of 51675 and 51680 is 5.

GCF(51675,51680) = 5

We will now calculate the prime factors of 51675 and 51680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51675 and 51680.

How to find the GCF of 51675 and 51680?

We will first find the prime factorization of 51675 and 51680. After we will calculate the factors of 51675 and 51680 and find the biggest common factor number .

Step-1: Prime Factorization of 51675

Prime factors of 51675 are 3, 5, 13, 53. Prime factorization of 51675 in exponential form is:

51675 = 3¹ × 5² × 13¹ × 53¹

Step-2: Prime Factorization of 51680

Prime factors of 51680 are 2, 5, 17, 19. Prime factorization of 51680 in exponential form is:

51680 = 2⁵ × 5¹ × 17¹ × 19¹

Step-3: Factors of 51675

List of positive integer factors of 51675 that divides 51675 without a remainder.

1, 3, 5, 13, 15, 25, 39, 53, 65, 75, 159, 195, 265, 325, 689, 795, 975, 1325, 2067, 3445, 3975, 10335, 17225

Step-4: Factors of 51680

List of positive integer factors of 51680 that divides 51675 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 19, 20, 32, 34, 38, 40, 68, 76, 80, 85, 95, 136, 152, 160, 170, 190, 272, 304, 323, 340, 380, 544, 608, 646, 680, 760, 1292, 1360, 1520, 1615, 2584, 2720, 3040, 3230, 5168, 6460, 10336, 12920, 25840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51675 and 51680. The biggest common factor number is the GCF number.
So the greatest common factor 51675 and 51680 is 5.

Also check out the Least Common Multiple of 51675 and 51680