What is the Greatest Common Factor of 51750 and 51765?

Greatest common factor (GCF) of 51750 and 51765 is 15.

GCF(51750,51765) = 15

We will now calculate the prime factors of 51750 and 51765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51750 and 51765.

How to find the GCF of 51750 and 51765?

We will first find the prime factorization of 51750 and 51765. After we will calculate the factors of 51750 and 51765 and find the biggest common factor number .

Step-1: Prime Factorization of 51750

Prime factors of 51750 are 2, 3, 5, 23. Prime factorization of 51750 in exponential form is:

51750 = 2¹ × 3² × 5³ × 23¹

Step-2: Prime Factorization of 51765

Prime factors of 51765 are 3, 5, 7, 17, 29. Prime factorization of 51765 in exponential form is:

51765 = 3¹ × 5¹ × 7¹ × 17¹ × 29¹

Step-3: Factors of 51750

List of positive integer factors of 51750 that divides 51750 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 25, 30, 45, 46, 50, 69, 75, 90, 115, 125, 138, 150, 207, 225, 230, 250, 345, 375, 414, 450, 575, 690, 750, 1035, 1125, 1150, 1725, 2070, 2250, 2875, 3450, 5175, 5750, 8625, 10350, 17250, 25875

Step-4: Factors of 51765

List of positive integer factors of 51765 that divides 51750 without a remainder.

1, 3, 5, 7, 15, 17, 21, 29, 35, 51, 85, 87, 105, 119, 145, 203, 255, 357, 435, 493, 595, 609, 1015, 1479, 1785, 2465, 3045, 3451, 7395, 10353, 17255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51750 and 51765. The biggest common factor number is the GCF number.
So the greatest common factor 51750 and 51765 is 15.

Also check out the Least Common Multiple of 51750 and 51765