What is the Greatest Common Factor of 25732 and 25746?

Greatest common factor (GCF) of 25732 and 25746 is 14.

GCF(25732,25746) = 14

We will now calculate the prime factors of 25732 and 25746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25732 and 25746.

How to find the GCF of 25732 and 25746?

We will first find the prime factorization of 25732 and 25746. After we will calculate the factors of 25732 and 25746 and find the biggest common factor number .

Step-1: Prime Factorization of 25732

Prime factors of 25732 are 2, 7, 919. Prime factorization of 25732 in exponential form is:

25732 = 2² × 7¹ × 919¹

Step-2: Prime Factorization of 25746

Prime factors of 25746 are 2, 3, 7, 613. Prime factorization of 25746 in exponential form is:

25746 = 2¹ × 3¹ × 7¹ × 613¹

Step-3: Factors of 25732

List of positive integer factors of 25732 that divides 25732 without a remainder.

1, 2, 4, 7, 14, 28, 919, 1838, 3676, 6433, 12866

Step-4: Factors of 25746

List of positive integer factors of 25746 that divides 25732 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 613, 1226, 1839, 3678, 4291, 8582, 12873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25732 and 25746. The biggest common factor number is the GCF number.
So the greatest common factor 25732 and 25746 is 14.

Also check out the Least Common Multiple of 25732 and 25746