What is the Greatest Common Factor of 51120 and 51140?

Greatest common factor (GCF) of 51120 and 51140 is 20.

GCF(51120,51140) = 20

We will now calculate the prime factors of 51120 and 51140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51120 and 51140.

How to find the GCF of 51120 and 51140?

We will first find the prime factorization of 51120 and 51140. After we will calculate the factors of 51120 and 51140 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 51140

Prime factors of 51140 are 2, 5, 2557. Prime factorization of 51140 in exponential form is:

51140 = 2² × 5¹ × 2557¹

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 51140

List of positive integer factors of 51140 that divides 51120 without a remainder.

1, 2, 4, 5, 10, 20, 2557, 5114, 10228, 12785, 25570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51120 and 51140. The biggest common factor number is the GCF number.
So the greatest common factor 51120 and 51140 is 20.

Also check out the Least Common Multiple of 51120 and 51140