What is the Greatest Common Factor of 25314 and 25320?

Greatest common factor (GCF) of 25314 and 25320 is 6.

GCF(25314,25320) = 6

We will now calculate the prime factors of 25314 and 25320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25314 and 25320.

How to find the GCF of 25314 and 25320?

We will first find the prime factorization of 25314 and 25320. After we will calculate the factors of 25314 and 25320 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 25320

Prime factors of 25320 are 2, 3, 5, 211. Prime factorization of 25320 in exponential form is:

25320 = 2³ × 3¹ × 5¹ × 211¹

Step-3: Factors of 25314

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

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

Step-4: Factors of 25320

List of positive integer factors of 25320 that divides 25314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 211, 422, 633, 844, 1055, 1266, 1688, 2110, 2532, 3165, 4220, 5064, 6330, 8440, 12660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25314 and 25320. The biggest common factor number is the GCF number.
So the greatest common factor 25314 and 25320 is 6.

Also check out the Least Common Multiple of 25314 and 25320