What is the Greatest Common Factor of 54225 and 54240?

Greatest common factor (GCF) of 54225 and 54240 is 15.

GCF(54225,54240) = 15

We will now calculate the prime factors of 54225 and 54240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54225 and 54240.

How to find the GCF of 54225 and 54240?

We will first find the prime factorization of 54225 and 54240. After we will calculate the factors of 54225 and 54240 and find the biggest common factor number .

Step-1: Prime Factorization of 54225

Prime factors of 54225 are 3, 5, 241. Prime factorization of 54225 in exponential form is:

54225 = 3² × 5² × 241¹

Step-2: Prime Factorization of 54240

Prime factors of 54240 are 2, 3, 5, 113. Prime factorization of 54240 in exponential form is:

54240 = 2⁵ × 3¹ × 5¹ × 113¹

Step-3: Factors of 54225

List of positive integer factors of 54225 that divides 54225 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 241, 723, 1205, 2169, 3615, 6025, 10845, 18075

Step-4: Factors of 54240

List of positive integer factors of 54240 that divides 54225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 113, 120, 160, 226, 240, 339, 452, 480, 565, 678, 904, 1130, 1356, 1695, 1808, 2260, 2712, 3390, 3616, 4520, 5424, 6780, 9040, 10848, 13560, 18080, 27120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54225 and 54240. The biggest common factor number is the GCF number.
So the greatest common factor 54225 and 54240 is 15.

Also check out the Least Common Multiple of 54225 and 54240