What is the Greatest Common Factor of 25774 and 25788?

Greatest common factor (GCF) of 25774 and 25788 is 14.

GCF(25774,25788) = 14

We will now calculate the prime factors of 25774 and 25788, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25774 and 25788.

How to find the GCF of 25774 and 25788?

We will first find the prime factorization of 25774 and 25788. After we will calculate the factors of 25774 and 25788 and find the biggest common factor number .

Step-1: Prime Factorization of 25774

Prime factors of 25774 are 2, 7, 263. Prime factorization of 25774 in exponential form is:

25774 = 2¹ × 7² × 263¹

Step-2: Prime Factorization of 25788

Prime factors of 25788 are 2, 3, 7, 307. Prime factorization of 25788 in exponential form is:

25788 = 2² × 3¹ × 7¹ × 307¹

Step-3: Factors of 25774

List of positive integer factors of 25774 that divides 25774 without a remainder.

1, 2, 7, 14, 49, 98, 263, 526, 1841, 3682, 12887

Step-4: Factors of 25788

List of positive integer factors of 25788 that divides 25774 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 307, 614, 921, 1228, 1842, 2149, 3684, 4298, 6447, 8596, 12894

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25774 and 25788. The biggest common factor number is the GCF number.
So the greatest common factor 25774 and 25788 is 14.

Also check out the Least Common Multiple of 25774 and 25788