What is the Greatest Common Factor of 25774 and 25789?

Greatest common factor (GCF) of 25774 and 25789 is 1.

GCF(25774,25789) = 1

We will now calculate the prime factors of 25774 and 25789, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25774 and 25789.

How to find the GCF of 25774 and 25789?

We will first find the prime factorization of 25774 and 25789. After we will calculate the factors of 25774 and 25789 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 25789

Prime factors of 25789 are 17, 37, 41. Prime factorization of 25789 in exponential form is:

25789 = 17¹ × 37¹ × 41¹

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 25789

List of positive integer factors of 25789 that divides 25774 without a remainder.

1, 17, 37, 41, 629, 697, 1517

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25774 and 25789. The biggest common factor number is the GCF number.
So the greatest common factor 25774 and 25789 is 1.

Also check out the Least Common Multiple of 25774 and 25789