What is the Greatest Common Factor of 25665 and 25680?

Greatest common factor (GCF) of 25665 and 25680 is 15.

GCF(25665,25680) = 15

We will now calculate the prime factors of 25665 and 25680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25665 and 25680.

How to find the GCF of 25665 and 25680?

We will first find the prime factorization of 25665 and 25680. After we will calculate the factors of 25665 and 25680 and find the biggest common factor number .

Step-1: Prime Factorization of 25665

Prime factors of 25665 are 3, 5, 29, 59. Prime factorization of 25665 in exponential form is:

25665 = 3¹ × 5¹ × 29¹ × 59¹

Step-2: Prime Factorization of 25680

Prime factors of 25680 are 2, 3, 5, 107. Prime factorization of 25680 in exponential form is:

25680 = 2⁴ × 3¹ × 5¹ × 107¹

Step-3: Factors of 25665

List of positive integer factors of 25665 that divides 25665 without a remainder.

1, 3, 5, 15, 29, 59, 87, 145, 177, 295, 435, 885, 1711, 5133, 8555

Step-4: Factors of 25680

List of positive integer factors of 25680 that divides 25665 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 107, 120, 214, 240, 321, 428, 535, 642, 856, 1070, 1284, 1605, 1712, 2140, 2568, 3210, 4280, 5136, 6420, 8560, 12840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25665 and 25680. The biggest common factor number is the GCF number.
So the greatest common factor 25665 and 25680 is 15.

Also check out the Least Common Multiple of 25665 and 25680