What is the Greatest Common Factor of 25721 and 25738?

Greatest common factor (GCF) of 25721 and 25738 is 17.

GCF(25721,25738) = 17

We will now calculate the prime factors of 25721 and 25738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25721 and 25738.

How to find the GCF of 25721 and 25738?

We will first find the prime factorization of 25721 and 25738. After we will calculate the factors of 25721 and 25738 and find the biggest common factor number .

Step-1: Prime Factorization of 25721

Prime factors of 25721 are 17, 89. Prime factorization of 25721 in exponential form is:

25721 = 17² × 89¹

Step-2: Prime Factorization of 25738

Prime factors of 25738 are 2, 17, 757. Prime factorization of 25738 in exponential form is:

25738 = 2¹ × 17¹ × 757¹

Step-3: Factors of 25721

List of positive integer factors of 25721 that divides 25721 without a remainder.

1, 17, 89, 289, 1513

Step-4: Factors of 25738

List of positive integer factors of 25738 that divides 25721 without a remainder.

1, 2, 17, 34, 757, 1514, 12869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25721 and 25738. The biggest common factor number is the GCF number.
So the greatest common factor 25721 and 25738 is 17.

Also check out the Least Common Multiple of 25721 and 25738