What is the Greatest Common Factor of 25760 and 25765?

Greatest common factor (GCF) of 25760 and 25765 is 5.

GCF(25760,25765) = 5

We will now calculate the prime factors of 25760 and 25765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25760 and 25765.

How to find the GCF of 25760 and 25765?

We will first find the prime factorization of 25760 and 25765. After we will calculate the factors of 25760 and 25765 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 25765

Prime factors of 25765 are 5, 5153. Prime factorization of 25765 in exponential form is:

25765 = 5¹ × 5153¹

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 25765

List of positive integer factors of 25765 that divides 25760 without a remainder.

1, 5, 5153

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25760 and 25765. The biggest common factor number is the GCF number.
So the greatest common factor 25760 and 25765 is 5.

Also check out the Least Common Multiple of 25760 and 25765