What is the Greatest Common Factor of 25774 and 25780?

Greatest common factor (GCF) of 25774 and 25780 is 2.

GCF(25774,25780) = 2

We will now calculate the prime factors of 25774 and 25780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25774 and 25780.

How to find the GCF of 25774 and 25780?

We will first find the prime factorization of 25774 and 25780. After we will calculate the factors of 25774 and 25780 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 25780

Prime factors of 25780 are 2, 5, 1289. Prime factorization of 25780 in exponential form is:

25780 = 2² × 5¹ × 1289¹

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 25780

List of positive integer factors of 25780 that divides 25774 without a remainder.

1, 2, 4, 5, 10, 20, 1289, 2578, 5156, 6445, 12890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25774 and 25780. The biggest common factor number is the GCF number.
So the greatest common factor 25774 and 25780 is 2.

Also check out the Least Common Multiple of 25774 and 25780