What is the Greatest Common Factor of 25216 and 25234?

Greatest common factor (GCF) of 25216 and 25234 is 2.

GCF(25216,25234) = 2

We will now calculate the prime factors of 25216 and 25234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25216 and 25234.

How to find the GCF of 25216 and 25234?

We will first find the prime factorization of 25216 and 25234. After we will calculate the factors of 25216 and 25234 and find the biggest common factor number .

Step-1: Prime Factorization of 25216

Prime factors of 25216 are 2, 197. Prime factorization of 25216 in exponential form is:

25216 = 2⁷ × 197¹

Step-2: Prime Factorization of 25234

Prime factors of 25234 are 2, 11, 31, 37. Prime factorization of 25234 in exponential form is:

25234 = 2¹ × 11¹ × 31¹ × 37¹

Step-3: Factors of 25216

List of positive integer factors of 25216 that divides 25216 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 197, 394, 788, 1576, 3152, 6304, 12608

Step-4: Factors of 25234

List of positive integer factors of 25234 that divides 25216 without a remainder.

1, 2, 11, 22, 31, 37, 62, 74, 341, 407, 682, 814, 1147, 2294, 12617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25216 and 25234. The biggest common factor number is the GCF number.
So the greatest common factor 25216 and 25234 is 2.

Also check out the Least Common Multiple of 25216 and 25234