What is the Greatest Common Factor of 53460 and 53475?

Greatest common factor (GCF) of 53460 and 53475 is 15.

GCF(53460,53475) = 15

We will now calculate the prime factors of 53460 and 53475, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53460 and 53475.

How to find the GCF of 53460 and 53475?

We will first find the prime factorization of 53460 and 53475. After we will calculate the factors of 53460 and 53475 and find the biggest common factor number .

Step-1: Prime Factorization of 53460

Prime factors of 53460 are 2, 3, 5, 11. Prime factorization of 53460 in exponential form is:

53460 = 2² × 3⁵ × 5¹ × 11¹

Step-2: Prime Factorization of 53475

Prime factors of 53475 are 3, 5, 23, 31. Prime factorization of 53475 in exponential form is:

53475 = 3¹ × 5² × 23¹ × 31¹

Step-3: Factors of 53460

List of positive integer factors of 53460 that divides 53460 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 81, 90, 99, 108, 110, 132, 135, 162, 165, 180, 198, 220, 243, 270, 297, 324, 330, 396, 405, 486, 495, 540, 594, 660, 810, 891, 972, 990, 1188, 1215, 1485, 1620, 1782, 1980, 2430, 2673, 2970, 3564, 4455, 4860, 5346, 5940, 8910, 10692, 13365, 17820, 26730

Step-4: Factors of 53475

List of positive integer factors of 53475 that divides 53460 without a remainder.

1, 3, 5, 15, 23, 25, 31, 69, 75, 93, 115, 155, 345, 465, 575, 713, 775, 1725, 2139, 2325, 3565, 10695, 17825

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53460 and 53475. The biggest common factor number is the GCF number.
So the greatest common factor 53460 and 53475 is 15.

Also check out the Least Common Multiple of 53460 and 53475