What is the Greatest Common Factor of 20896 and 20914?

Greatest common factor (GCF) of 20896 and 20914 is 2.

GCF(20896,20914) = 2

We will now calculate the prime factors of 20896 and 20914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20896 and 20914.

How to find the GCF of 20896 and 20914?

We will first find the prime factorization of 20896 and 20914. After we will calculate the factors of 20896 and 20914 and find the biggest common factor number .

Step-1: Prime Factorization of 20896

Prime factors of 20896 are 2, 653. Prime factorization of 20896 in exponential form is:

20896 = 2⁵ × 653¹

Step-2: Prime Factorization of 20914

Prime factors of 20914 are 2, 10457. Prime factorization of 20914 in exponential form is:

20914 = 2¹ × 10457¹

Step-3: Factors of 20896

List of positive integer factors of 20896 that divides 20896 without a remainder.

1, 2, 4, 8, 16, 32, 653, 1306, 2612, 5224, 10448

Step-4: Factors of 20914

List of positive integer factors of 20914 that divides 20896 without a remainder.

1, 2, 10457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20896 and 20914. The biggest common factor number is the GCF number.
So the greatest common factor 20896 and 20914 is 2.

Also check out the Least Common Multiple of 20896 and 20914