What is the Greatest Common Factor of 53754 and 53760?

Greatest common factor (GCF) of 53754 and 53760 is 6.

GCF(53754,53760) = 6

We will now calculate the prime factors of 53754 and 53760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53754 and 53760.

How to find the GCF of 53754 and 53760?

We will first find the prime factorization of 53754 and 53760. After we will calculate the factors of 53754 and 53760 and find the biggest common factor number .

Step-1: Prime Factorization of 53754

Prime factors of 53754 are 2, 3, 17, 31. Prime factorization of 53754 in exponential form is:

53754 = 2¹ × 3¹ × 17² × 31¹

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 53754

List of positive integer factors of 53754 that divides 53754 without a remainder.

1, 2, 3, 6, 17, 31, 34, 51, 62, 93, 102, 186, 289, 527, 578, 867, 1054, 1581, 1734, 3162, 8959, 17918, 26877

Step-4: Factors of 53760

List of positive integer factors of 53760 that divides 53754 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 53754 and 53760. The biggest common factor number is the GCF number.
So the greatest common factor 53754 and 53760 is 6.

Also check out the Least Common Multiple of 53754 and 53760