What is the Greatest Common Factor of 53748 and 53760?

Greatest common factor (GCF) of 53748 and 53760 is 12.

GCF(53748,53760) = 12

We will now calculate the prime factors of 53748 and 53760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53748 and 53760.

How to find the GCF of 53748 and 53760?

We will first find the prime factorization of 53748 and 53760. After we will calculate the factors of 53748 and 53760 and find the biggest common factor number .

Step-1: Prime Factorization of 53748

Prime factors of 53748 are 2, 3, 1493. Prime factorization of 53748 in exponential form is:

53748 = 2² × 3² × 1493¹

Step-2: Prime Factorization of 53760

Prime factors of 53760 are 2, 3, 5, 7. Prime factorization of 53760 in exponential form is:

53760 = 2⁹ × 3¹ × 5¹ × 7¹

Step-3: Factors of 53748

List of positive integer factors of 53748 that divides 53748 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1493, 2986, 4479, 5972, 8958, 13437, 17916, 26874

Step-4: Factors of 53760

List of positive integer factors of 53760 that divides 53748 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 256, 280, 320, 336, 384, 420, 448, 480, 512, 560, 640, 672, 768, 840, 896, 960, 1120, 1280, 1344, 1536, 1680, 1792, 1920, 2240, 2560, 2688, 3360, 3584, 3840, 4480, 5376, 6720, 7680, 8960, 10752, 13440, 17920, 26880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53748 and 53760. The biggest common factor number is the GCF number.
So the greatest common factor 53748 and 53760 is 12.

Also check out the Least Common Multiple of 53748 and 53760