What is the Greatest Common Factor of 25714 and 25732?

Greatest common factor (GCF) of 25714 and 25732 is 2.

GCF(25714,25732) = 2

We will now calculate the prime factors of 25714 and 25732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25714 and 25732.

How to find the GCF of 25714 and 25732?

We will first find the prime factorization of 25714 and 25732. After we will calculate the factors of 25714 and 25732 and find the biggest common factor number .

Step-1: Prime Factorization of 25714

Prime factors of 25714 are 2, 13, 23, 43. Prime factorization of 25714 in exponential form is:

25714 = 2¹ × 13¹ × 23¹ × 43¹

Step-2: 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-3: Factors of 25714

List of positive integer factors of 25714 that divides 25714 without a remainder.

1, 2, 13, 23, 26, 43, 46, 86, 299, 559, 598, 989, 1118, 1978, 12857

Step-4: Factors of 25732

List of positive integer factors of 25732 that divides 25714 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25714 and 25732. The biggest common factor number is the GCF number.
So the greatest common factor 25714 and 25732 is 2.

Also check out the Least Common Multiple of 25714 and 25732