What is the Greatest Common Factor of 85760 and 85774?

Greatest common factor (GCF) of 85760 and 85774 is 2.

GCF(85760,85774) = 2

We will now calculate the prime factors of 85760 and 85774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85760 and 85774.

How to find the GCF of 85760 and 85774?

We will first find the prime factorization of 85760 and 85774. After we will calculate the factors of 85760 and 85774 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 85774

Prime factors of 85774 are 2, 13, 3299. Prime factorization of 85774 in exponential form is:

85774 = 2¹ × 13¹ × 3299¹

Step-3: Factors of 85760

List of positive integer factors of 85760 that divides 85760 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

Step-4: Factors of 85774

List of positive integer factors of 85774 that divides 85760 without a remainder.

1, 2, 13, 26, 3299, 6598, 42887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85760 and 85774. The biggest common factor number is the GCF number.
So the greatest common factor 85760 and 85774 is 2.

Also check out the Least Common Multiple of 85760 and 85774