What is the Greatest Common Factor of 53940 and 53952?

Greatest common factor (GCF) of 53940 and 53952 is 12.

GCF(53940,53952) = 12

We will now calculate the prime factors of 53940 and 53952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53940 and 53952.

How to find the GCF of 53940 and 53952?

We will first find the prime factorization of 53940 and 53952. After we will calculate the factors of 53940 and 53952 and find the biggest common factor number .

Step-1: Prime Factorization of 53940

Prime factors of 53940 are 2, 3, 5, 29, 31. Prime factorization of 53940 in exponential form is:

53940 = 2² × 3¹ × 5¹ × 29¹ × 31¹

Step-2: Prime Factorization of 53952

Prime factors of 53952 are 2, 3, 281. Prime factorization of 53952 in exponential form is:

53952 = 2⁶ × 3¹ × 281¹

Step-3: Factors of 53940

List of positive integer factors of 53940 that divides 53940 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 31, 58, 60, 62, 87, 93, 116, 124, 145, 155, 174, 186, 290, 310, 348, 372, 435, 465, 580, 620, 870, 899, 930, 1740, 1798, 1860, 2697, 3596, 4495, 5394, 8990, 10788, 13485, 17980, 26970

Step-4: Factors of 53952

List of positive integer factors of 53952 that divides 53940 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 281, 562, 843, 1124, 1686, 2248, 3372, 4496, 6744, 8992, 13488, 17984, 26976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53940 and 53952. The biggest common factor number is the GCF number.
So the greatest common factor 53940 and 53952 is 12.

Also check out the Least Common Multiple of 53940 and 53952