What is the Greatest Common Factor of 51114 and 51120?

Greatest common factor (GCF) of 51114 and 51120 is 6.

GCF(51114,51120) = 6

We will now calculate the prime factors of 51114 and 51120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51114 and 51120.

How to find the GCF of 51114 and 51120?

We will first find the prime factorization of 51114 and 51120. After we will calculate the factors of 51114 and 51120 and find the biggest common factor number .

Step-1: Prime Factorization of 51114

Prime factors of 51114 are 2, 3, 7, 1217. Prime factorization of 51114 in exponential form is:

51114 = 2¹ × 3¹ × 7¹ × 1217¹

Step-2: 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-3: Factors of 51114

List of positive integer factors of 51114 that divides 51114 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1217, 2434, 3651, 7302, 8519, 17038, 25557

Step-4: Factors of 51120

List of positive integer factors of 51120 that divides 51114 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51114 and 51120. The biggest common factor number is the GCF number.
So the greatest common factor 51114 and 51120 is 6.

Also check out the Least Common Multiple of 51114 and 51120