What is the Greatest Common Factor of 51120 and 51125?

Greatest common factor (GCF) of 51120 and 51125 is 5.

GCF(51120,51125) = 5

We will now calculate the prime factors of 51120 and 51125, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51120 and 51125.

How to find the GCF of 51120 and 51125?

We will first find the prime factorization of 51120 and 51125. After we will calculate the factors of 51120 and 51125 and find the biggest common factor number .

Step-1: Prime Factorization of 51120

Prime factors of 51120 are 2, 3, 5, 71. Prime factorization of 51120 in exponential form is:

51120 = 2⁴ × 3² × 5¹ × 71¹

Step-2: Prime Factorization of 51125

Prime factors of 51125 are 5, 409. Prime factorization of 51125 in exponential form is:

51125 = 5³ × 409¹

Step-3: Factors of 51120

List of positive integer factors of 51120 that divides 51120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 71, 72, 80, 90, 120, 142, 144, 180, 213, 240, 284, 355, 360, 426, 568, 639, 710, 720, 852, 1065, 1136, 1278, 1420, 1704, 2130, 2556, 2840, 3195, 3408, 4260, 5112, 5680, 6390, 8520, 10224, 12780, 17040, 25560

Step-4: Factors of 51125

List of positive integer factors of 51125 that divides 51120 without a remainder.

1, 5, 25, 125, 409, 2045, 10225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51120 and 51125. The biggest common factor number is the GCF number.
So the greatest common factor 51120 and 51125 is 5.

Also check out the Least Common Multiple of 51120 and 51125