What is the Greatest Common Factor of 25678 and 25696?

Greatest common factor (GCF) of 25678 and 25696 is 2.

GCF(25678,25696) = 2

We will now calculate the prime factors of 25678 and 25696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25678 and 25696.

How to find the GCF of 25678 and 25696?

We will first find the prime factorization of 25678 and 25696. After we will calculate the factors of 25678 and 25696 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 25696

Prime factors of 25696 are 2, 11, 73. Prime factorization of 25696 in exponential form is:

25696 = 2⁵ × 11¹ × 73¹

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 25696

List of positive integer factors of 25696 that divides 25678 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 73, 88, 146, 176, 292, 352, 584, 803, 1168, 1606, 2336, 3212, 6424, 12848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25678 and 25696. The biggest common factor number is the GCF number.
So the greatest common factor 25678 and 25696 is 2.

Also check out the Least Common Multiple of 25678 and 25696