What is the Greatest Common Factor of 53760 and 53766?

Greatest common factor (GCF) of 53760 and 53766 is 6.

GCF(53760,53766) = 6

We will now calculate the prime factors of 53760 and 53766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53760 and 53766.

How to find the GCF of 53760 and 53766?

We will first find the prime factorization of 53760 and 53766. After we will calculate the factors of 53760 and 53766 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 53766

Prime factors of 53766 are 2, 3, 29, 103. Prime factorization of 53766 in exponential form is:

53766 = 2¹ × 3² × 29¹ × 103¹

Step-3: Factors of 53760

List of positive integer factors of 53760 that divides 53760 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

Step-4: Factors of 53766

List of positive integer factors of 53766 that divides 53760 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 103, 174, 206, 261, 309, 522, 618, 927, 1854, 2987, 5974, 8961, 17922, 26883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53760 and 53766. The biggest common factor number is the GCF number.
So the greatest common factor 53760 and 53766 is 6.

Also check out the Least Common Multiple of 53760 and 53766