What is the Greatest Common Factor of 54075 and 54080?

Greatest common factor (GCF) of 54075 and 54080 is 5.

GCF(54075,54080) = 5

We will now calculate the prime factors of 54075 and 54080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54075 and 54080.

How to find the GCF of 54075 and 54080?

We will first find the prime factorization of 54075 and 54080. After we will calculate the factors of 54075 and 54080 and find the biggest common factor number .

Step-1: Prime Factorization of 54075

Prime factors of 54075 are 3, 5, 7, 103. Prime factorization of 54075 in exponential form is:

54075 = 3¹ × 5² × 7¹ × 103¹

Step-2: Prime Factorization of 54080

Prime factors of 54080 are 2, 5, 13. Prime factorization of 54080 in exponential form is:

54080 = 2⁶ × 5¹ × 13²

Step-3: Factors of 54075

List of positive integer factors of 54075 that divides 54075 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 103, 105, 175, 309, 515, 525, 721, 1545, 2163, 2575, 3605, 7725, 10815, 18025

Step-4: Factors of 54080

List of positive integer factors of 54080 that divides 54075 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 64, 65, 80, 104, 130, 160, 169, 208, 260, 320, 338, 416, 520, 676, 832, 845, 1040, 1352, 1690, 2080, 2704, 3380, 4160, 5408, 6760, 10816, 13520, 27040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54075 and 54080. The biggest common factor number is the GCF number.
So the greatest common factor 54075 and 54080 is 5.

Also check out the Least Common Multiple of 54075 and 54080