What is the Greatest Common Factor of 25970 and 25977?

Greatest common factor (GCF) of 25970 and 25977 is 7.

GCF(25970,25977) = 7

We will now calculate the prime factors of 25970 and 25977, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25970 and 25977.

How to find the GCF of 25970 and 25977?

We will first find the prime factorization of 25970 and 25977. After we will calculate the factors of 25970 and 25977 and find the biggest common factor number .

Step-1: Prime Factorization of 25970

Prime factors of 25970 are 2, 5, 7, 53. Prime factorization of 25970 in exponential form is:

25970 = 2¹ × 5¹ × 7² × 53¹

Step-2: Prime Factorization of 25977

Prime factors of 25977 are 3, 7, 1237. Prime factorization of 25977 in exponential form is:

25977 = 3¹ × 7¹ × 1237¹

Step-3: Factors of 25970

List of positive integer factors of 25970 that divides 25970 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 53, 70, 98, 106, 245, 265, 371, 490, 530, 742, 1855, 2597, 3710, 5194, 12985

Step-4: Factors of 25977

List of positive integer factors of 25977 that divides 25970 without a remainder.

1, 3, 7, 21, 1237, 3711, 8659

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25970 and 25977. The biggest common factor number is the GCF number.
So the greatest common factor 25970 and 25977 is 7.

Also check out the Least Common Multiple of 25970 and 25977