What is the Greatest Common Factor of 25296 and 25314?

Greatest common factor (GCF) of 25296 and 25314 is 6.

GCF(25296,25314) = 6

We will now calculate the prime factors of 25296 and 25314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25296 and 25314.

How to find the GCF of 25296 and 25314?

We will first find the prime factorization of 25296 and 25314. After we will calculate the factors of 25296 and 25314 and find the biggest common factor number .

Step-1: Prime Factorization of 25296

Prime factors of 25296 are 2, 3, 17, 31. Prime factorization of 25296 in exponential form is:

25296 = 2⁴ × 3¹ × 17¹ × 31¹

Step-2: Prime Factorization of 25314

Prime factors of 25314 are 2, 3, 4219. Prime factorization of 25314 in exponential form is:

25314 = 2¹ × 3¹ × 4219¹

Step-3: Factors of 25296

List of positive integer factors of 25296 that divides 25296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 31, 34, 48, 51, 62, 68, 93, 102, 124, 136, 186, 204, 248, 272, 372, 408, 496, 527, 744, 816, 1054, 1488, 1581, 2108, 3162, 4216, 6324, 8432, 12648

Step-4: Factors of 25314

List of positive integer factors of 25314 that divides 25296 without a remainder.

1, 2, 3, 6, 4219, 8438, 12657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25296 and 25314. The biggest common factor number is the GCF number.
So the greatest common factor 25296 and 25314 is 6.

Also check out the Least Common Multiple of 25296 and 25314