What is the Greatest Common Factor of 25760 and 25767?

Greatest common factor (GCF) of 25760 and 25767 is 7.

GCF(25760,25767) = 7

We will now calculate the prime factors of 25760 and 25767, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25760 and 25767.

How to find the GCF of 25760 and 25767?

We will first find the prime factorization of 25760 and 25767. After we will calculate the factors of 25760 and 25767 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 25767

Prime factors of 25767 are 3, 7, 409. Prime factorization of 25767 in exponential form is:

25767 = 3² × 7¹ × 409¹

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 25767

List of positive integer factors of 25767 that divides 25760 without a remainder.

1, 3, 7, 9, 21, 63, 409, 1227, 2863, 3681, 8589

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25760 and 25767. The biggest common factor number is the GCF number.
So the greatest common factor 25760 and 25767 is 7.

Also check out the Least Common Multiple of 25760 and 25767