What is the Greatest Common Factor of 54825 and 54840?

Greatest common factor (GCF) of 54825 and 54840 is 15.

GCF(54825,54840) = 15

We will now calculate the prime factors of 54825 and 54840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54825 and 54840.

How to find the GCF of 54825 and 54840?

We will first find the prime factorization of 54825 and 54840. After we will calculate the factors of 54825 and 54840 and find the biggest common factor number .

Step-1: Prime Factorization of 54825

Prime factors of 54825 are 3, 5, 17, 43. Prime factorization of 54825 in exponential form is:

54825 = 3¹ × 5² × 17¹ × 43¹

Step-2: Prime Factorization of 54840

Prime factors of 54840 are 2, 3, 5, 457. Prime factorization of 54840 in exponential form is:

54840 = 2³ × 3¹ × 5¹ × 457¹

Step-3: Factors of 54825

List of positive integer factors of 54825 that divides 54825 without a remainder.

1, 3, 5, 15, 17, 25, 43, 51, 75, 85, 129, 215, 255, 425, 645, 731, 1075, 1275, 2193, 3225, 3655, 10965, 18275

Step-4: Factors of 54840

List of positive integer factors of 54840 that divides 54825 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 457, 914, 1371, 1828, 2285, 2742, 3656, 4570, 5484, 6855, 9140, 10968, 13710, 18280, 27420

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54825 and 54840. The biggest common factor number is the GCF number.
So the greatest common factor 54825 and 54840 is 15.

Also check out the Least Common Multiple of 54825 and 54840