What is the Greatest Common Factor of 85744 and 85760?

Greatest common factor (GCF) of 85744 and 85760 is 16.

GCF(85744,85760) = 16

We will now calculate the prime factors of 85744 and 85760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85744 and 85760.

How to find the GCF of 85744 and 85760?

We will first find the prime factorization of 85744 and 85760. After we will calculate the factors of 85744 and 85760 and find the biggest common factor number .

Step-1: Prime Factorization of 85744

Prime factors of 85744 are 2, 23, 233. Prime factorization of 85744 in exponential form is:

85744 = 2⁴ × 23¹ × 233¹

Step-2: Prime Factorization of 85760

Prime factors of 85760 are 2, 5, 67. Prime factorization of 85760 in exponential form is:

85760 = 2⁸ × 5¹ × 67¹

Step-3: Factors of 85744

List of positive integer factors of 85744 that divides 85744 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 184, 233, 368, 466, 932, 1864, 3728, 5359, 10718, 21436, 42872

Step-4: Factors of 85760

List of positive integer factors of 85760 that divides 85744 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 67, 80, 128, 134, 160, 256, 268, 320, 335, 536, 640, 670, 1072, 1280, 1340, 2144, 2680, 4288, 5360, 8576, 10720, 17152, 21440, 42880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85744 and 85760. The biggest common factor number is the GCF number.
So the greatest common factor 85744 and 85760 is 16.

Also check out the Least Common Multiple of 85744 and 85760