What is the Greatest Common Factor of 25296 and 25302?

Greatest common factor (GCF) of 25296 and 25302 is 6.

GCF(25296,25302) = 6

We will now calculate the prime factors of 25296 and 25302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25296 and 25302.

How to find the GCF of 25296 and 25302?

We will first find the prime factorization of 25296 and 25302. After we will calculate the factors of 25296 and 25302 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 25302

Prime factors of 25302 are 2, 3, 4217. Prime factorization of 25302 in exponential form is:

25302 = 2¹ × 3¹ × 4217¹

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 25302

List of positive integer factors of 25302 that divides 25296 without a remainder.

1, 2, 3, 6, 4217, 8434, 12651

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25296 and 25302. The biggest common factor number is the GCF number.
So the greatest common factor 25296 and 25302 is 6.

Also check out the Least Common Multiple of 25296 and 25302