What is the Greatest Common Factor of 25746 and 25760?

Greatest common factor (GCF) of 25746 and 25760 is 14.

GCF(25746,25760) = 14

We will now calculate the prime factors of 25746 and 25760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25746 and 25760.

How to find the GCF of 25746 and 25760?

We will first find the prime factorization of 25746 and 25760. After we will calculate the factors of 25746 and 25760 and find the biggest common factor number .

Step-1: Prime Factorization of 25746

Prime factors of 25746 are 2, 3, 7, 613. Prime factorization of 25746 in exponential form is:

25746 = 2¹ × 3¹ × 7¹ × 613¹

Step-2: 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-3: Factors of 25746

List of positive integer factors of 25746 that divides 25746 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 613, 1226, 1839, 3678, 4291, 8582, 12873

Step-4: Factors of 25760

List of positive integer factors of 25760 that divides 25746 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25746 and 25760. The biggest common factor number is the GCF number.
So the greatest common factor 25746 and 25760 is 14.

Also check out the Least Common Multiple of 25746 and 25760