What is the Greatest Common Factor of 25734 and 25742?

Greatest common factor (GCF) of 25734 and 25742 is 2.

GCF(25734,25742) = 2

We will now calculate the prime factors of 25734 and 25742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25734 and 25742.

How to find the GCF of 25734 and 25742?

We will first find the prime factorization of 25734 and 25742. After we will calculate the factors of 25734 and 25742 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 25742

Prime factors of 25742 are 2, 61, 211. Prime factorization of 25742 in exponential form is:

25742 = 2¹ × 61¹ × 211¹

Step-3: Factors of 25734

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

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

Step-4: Factors of 25742

List of positive integer factors of 25742 that divides 25734 without a remainder.

1, 2, 61, 122, 211, 422, 12871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25734 and 25742. The biggest common factor number is the GCF number.
So the greatest common factor 25734 and 25742 is 2.

Also check out the Least Common Multiple of 25734 and 25742