What is the Greatest Common Factor of 25748 and 25762?

Greatest common factor (GCF) of 25748 and 25762 is 2.

GCF(25748,25762) = 2

We will now calculate the prime factors of 25748 and 25762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25748 and 25762.

How to find the GCF of 25748 and 25762?

We will first find the prime factorization of 25748 and 25762. After we will calculate the factors of 25748 and 25762 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 25762

Prime factors of 25762 are 2, 11, 1171. Prime factorization of 25762 in exponential form is:

25762 = 2¹ × 11¹ × 1171¹

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 25762

List of positive integer factors of 25762 that divides 25748 without a remainder.

1, 2, 11, 22, 1171, 2342, 12881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25748 and 25762. The biggest common factor number is the GCF number.
So the greatest common factor 25748 and 25762 is 2.

Also check out the Least Common Multiple of 25748 and 25762