What is the Greatest Common Factor of 25814 and 25824?

Greatest common factor (GCF) of 25814 and 25824 is 2.

GCF(25814,25824) = 2

We will now calculate the prime factors of 25814 and 25824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25814 and 25824.

How to find the GCF of 25814 and 25824?

We will first find the prime factorization of 25814 and 25824. After we will calculate the factors of 25814 and 25824 and find the biggest common factor number .

Step-1: Prime Factorization of 25814

Prime factors of 25814 are 2, 12907. Prime factorization of 25814 in exponential form is:

25814 = 2¹ × 12907¹

Step-2: 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-3: Factors of 25814

List of positive integer factors of 25814 that divides 25814 without a remainder.

1, 2, 12907

Step-4: Factors of 25824

List of positive integer factors of 25824 that divides 25814 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25814 and 25824. The biggest common factor number is the GCF number.
So the greatest common factor 25814 and 25824 is 2.

Also check out the Least Common Multiple of 25814 and 25824