What is the Greatest Common Factor of 25696 and 25714?

Greatest common factor (GCF) of 25696 and 25714 is 2.

GCF(25696,25714) = 2

We will now calculate the prime factors of 25696 and 25714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25696 and 25714.

How to find the GCF of 25696 and 25714?

We will first find the prime factorization of 25696 and 25714. After we will calculate the factors of 25696 and 25714 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 25714

Prime factors of 25714 are 2, 13, 23, 43. Prime factorization of 25714 in exponential form is:

25714 = 2¹ × 13¹ × 23¹ × 43¹

Step-3: Factors of 25696

List of positive integer factors of 25696 that divides 25696 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

Step-4: Factors of 25714

List of positive integer factors of 25714 that divides 25696 without a remainder.

1, 2, 13, 23, 26, 43, 46, 86, 299, 559, 598, 989, 1118, 1978, 12857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25696 and 25714. The biggest common factor number is the GCF number.
So the greatest common factor 25696 and 25714 is 2.

Also check out the Least Common Multiple of 25696 and 25714