What is the Greatest Common Factor of 25725 and 25734?

Greatest common factor (GCF) of 25725 and 25734 is 3.

GCF(25725,25734) = 3

We will now calculate the prime factors of 25725 and 25734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25725 and 25734.

How to find the GCF of 25725 and 25734?

We will first find the prime factorization of 25725 and 25734. After we will calculate the factors of 25725 and 25734 and find the biggest common factor number .

Step-1: Prime Factorization of 25725

Prime factors of 25725 are 3, 5, 7. Prime factorization of 25725 in exponential form is:

25725 = 3¹ × 5² × 7³

Step-2: Prime Factorization of 25734

Prime factors of 25734 are 2, 3, 4289. Prime factorization of 25734 in exponential form is:

25734 = 2¹ × 3¹ × 4289¹

Step-3: Factors of 25725

List of positive integer factors of 25725 that divides 25725 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 343, 525, 735, 1029, 1225, 1715, 3675, 5145, 8575

Step-4: Factors of 25734

List of positive integer factors of 25734 that divides 25725 without a remainder.

1, 2, 3, 6, 4289, 8578, 12867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25725 and 25734. The biggest common factor number is the GCF number.
So the greatest common factor 25725 and 25734 is 3.

Also check out the Least Common Multiple of 25725 and 25734