What is the Greatest Common Factor of 53760 and 53780?

Greatest common factor (GCF) of 53760 and 53780 is 20.

GCF(53760,53780) = 20

We will now calculate the prime factors of 53760 and 53780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53760 and 53780.

How to find the GCF of 53760 and 53780?

We will first find the prime factorization of 53760 and 53780. After we will calculate the factors of 53760 and 53780 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 53780

Prime factors of 53780 are 2, 5, 2689. Prime factorization of 53780 in exponential form is:

53780 = 2² × 5¹ × 2689¹

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 53780

List of positive integer factors of 53780 that divides 53760 without a remainder.

1, 2, 4, 5, 10, 20, 2689, 5378, 10756, 13445, 26890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53760 and 53780. The biggest common factor number is the GCF number.
So the greatest common factor 53760 and 53780 is 20.

Also check out the Least Common Multiple of 53760 and 53780