What is the Greatest Common Factor of 25748 and 25766?

Greatest common factor (GCF) of 25748 and 25766 is 2.

GCF(25748,25766) = 2

We will now calculate the prime factors of 25748 and 25766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25748 and 25766.

How to find the GCF of 25748 and 25766?

We will first find the prime factorization of 25748 and 25766. After we will calculate the factors of 25748 and 25766 and find the biggest common factor number .

Step-1: Prime Factorization of 25748

Prime factors of 25748 are 2, 41, 157. Prime factorization of 25748 in exponential form is:

25748 = 2² × 41¹ × 157¹

Step-2: Prime Factorization of 25766

Prime factors of 25766 are 2, 13, 991. Prime factorization of 25766 in exponential form is:

25766 = 2¹ × 13¹ × 991¹

Step-3: Factors of 25748

List of positive integer factors of 25748 that divides 25748 without a remainder.

1, 2, 4, 41, 82, 157, 164, 314, 628, 6437, 12874

Step-4: Factors of 25766

List of positive integer factors of 25766 that divides 25748 without a remainder.

1, 2, 13, 26, 991, 1982, 12883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25748 and 25766. The biggest common factor number is the GCF number.
So the greatest common factor 25748 and 25766 is 2.

Also check out the Least Common Multiple of 25748 and 25766