What is the Greatest Common Factor of 25760 and 25768?

Greatest common factor (GCF) of 25760 and 25768 is 8.

GCF(25760,25768) = 8

We will now calculate the prime factors of 25760 and 25768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25760 and 25768.

How to find the GCF of 25760 and 25768?

We will first find the prime factorization of 25760 and 25768. After we will calculate the factors of 25760 and 25768 and find the biggest common factor number .

Step-1: Prime Factorization of 25760

Prime factors of 25760 are 2, 5, 7, 23. Prime factorization of 25760 in exponential form is:

25760 = 2⁵ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 25768

Prime factors of 25768 are 2, 3221. Prime factorization of 25768 in exponential form is:

25768 = 2³ × 3221¹

Step-3: Factors of 25760

List of positive integer factors of 25760 that divides 25760 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 23, 28, 32, 35, 40, 46, 56, 70, 80, 92, 112, 115, 140, 160, 161, 184, 224, 230, 280, 322, 368, 460, 560, 644, 736, 805, 920, 1120, 1288, 1610, 1840, 2576, 3220, 3680, 5152, 6440, 12880

Step-4: Factors of 25768

List of positive integer factors of 25768 that divides 25760 without a remainder.

1, 2, 4, 8, 3221, 6442, 12884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25760 and 25768. The biggest common factor number is the GCF number.
So the greatest common factor 25760 and 25768 is 8.

Also check out the Least Common Multiple of 25760 and 25768