What is the Greatest Common Factor of 25298 and 25312?

Greatest common factor (GCF) of 25298 and 25312 is 14.

GCF(25298,25312) = 14

We will now calculate the prime factors of 25298 and 25312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25298 and 25312.

How to find the GCF of 25298 and 25312?

We will first find the prime factorization of 25298 and 25312. After we will calculate the factors of 25298 and 25312 and find the biggest common factor number .

Step-1: Prime Factorization of 25298

Prime factors of 25298 are 2, 7, 13, 139. Prime factorization of 25298 in exponential form is:

25298 = 2¹ × 7¹ × 13¹ × 139¹

Step-2: Prime Factorization of 25312

Prime factors of 25312 are 2, 7, 113. Prime factorization of 25312 in exponential form is:

25312 = 2⁵ × 7¹ × 113¹

Step-3: Factors of 25298

List of positive integer factors of 25298 that divides 25298 without a remainder.

1, 2, 7, 13, 14, 26, 91, 139, 182, 278, 973, 1807, 1946, 3614, 12649

Step-4: Factors of 25312

List of positive integer factors of 25312 that divides 25298 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 113, 224, 226, 452, 791, 904, 1582, 1808, 3164, 3616, 6328, 12656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25298 and 25312. The biggest common factor number is the GCF number.
So the greatest common factor 25298 and 25312 is 14.

Also check out the Least Common Multiple of 25298 and 25312