What is the Greatest Common Factor of 53760 and 53765?

Greatest common factor (GCF) of 53760 and 53765 is 5.

GCF(53760,53765) = 5

We will now calculate the prime factors of 53760 and 53765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53760 and 53765.

How to find the GCF of 53760 and 53765?

We will first find the prime factorization of 53760 and 53765. After we will calculate the factors of 53760 and 53765 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 53765

Prime factors of 53765 are 5, 10753. Prime factorization of 53765 in exponential form is:

53765 = 5¹ × 10753¹

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 53765

List of positive integer factors of 53765 that divides 53760 without a remainder.

1, 5, 10753

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53760 and 53765. The biggest common factor number is the GCF number.
So the greatest common factor 53760 and 53765 is 5.

Also check out the Least Common Multiple of 53760 and 53765