What is the Greatest Common Factor of 25678 and 25688?

Greatest common factor (GCF) of 25678 and 25688 is 2.

GCF(25678,25688) = 2

We will now calculate the prime factors of 25678 and 25688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25678 and 25688.

How to find the GCF of 25678 and 25688?

We will first find the prime factorization of 25678 and 25688. After we will calculate the factors of 25678 and 25688 and find the biggest common factor number .

Step-1: Prime Factorization of 25678

Prime factors of 25678 are 2, 37, 347. Prime factorization of 25678 in exponential form is:

25678 = 2¹ × 37¹ × 347¹

Step-2: Prime Factorization of 25688

Prime factors of 25688 are 2, 13, 19. Prime factorization of 25688 in exponential form is:

25688 = 2³ × 13² × 19¹

Step-3: Factors of 25678

List of positive integer factors of 25678 that divides 25678 without a remainder.

1, 2, 37, 74, 347, 694, 12839

Step-4: Factors of 25688

List of positive integer factors of 25688 that divides 25678 without a remainder.

1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 169, 247, 338, 494, 676, 988, 1352, 1976, 3211, 6422, 12844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25678 and 25688. The biggest common factor number is the GCF number.
So the greatest common factor 25678 and 25688 is 2.

Also check out the Least Common Multiple of 25678 and 25688