What is the Greatest Common Factor of 25824 and 25830?

Greatest common factor (GCF) of 25824 and 25830 is 6.

GCF(25824,25830) = 6

We will now calculate the prime factors of 25824 and 25830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25824 and 25830.

How to find the GCF of 25824 and 25830?

We will first find the prime factorization of 25824 and 25830. After we will calculate the factors of 25824 and 25830 and find the biggest common factor number .

Step-1: Prime Factorization of 25824

Prime factors of 25824 are 2, 3, 269. Prime factorization of 25824 in exponential form is:

25824 = 2⁵ × 3¹ × 269¹

Step-2: Prime Factorization of 25830

Prime factors of 25830 are 2, 3, 5, 7, 41. Prime factorization of 25830 in exponential form is:

25830 = 2¹ × 3² × 5¹ × 7¹ × 41¹

Step-3: Factors of 25824

List of positive integer factors of 25824 that divides 25824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 269, 538, 807, 1076, 1614, 2152, 3228, 4304, 6456, 8608, 12912

Step-4: Factors of 25830

List of positive integer factors of 25830 that divides 25824 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 41, 42, 45, 63, 70, 82, 90, 105, 123, 126, 205, 210, 246, 287, 315, 369, 410, 574, 615, 630, 738, 861, 1230, 1435, 1722, 1845, 2583, 2870, 3690, 4305, 5166, 8610, 12915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25824 and 25830. The biggest common factor number is the GCF number.
So the greatest common factor 25824 and 25830 is 6.

Also check out the Least Common Multiple of 25824 and 25830