What is the Greatest Common Factor of 896 and 914?

Greatest common factor (GCF) of 896 and 914 is 2.

GCF(896,914) = 2

We will now calculate the prime factors of 896 and 914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 896 and 914.

How to find the GCF of 896 and 914?

We will first find the prime factorization of 896 and 914. After we will calculate the factors of 896 and 914 and find the biggest common factor number .

Step-1: Prime Factorization of 896

Prime factors of 896 are 2, 7. Prime factorization of 896 in exponential form is:

896 = 2⁷ × 7¹

Step-2: Prime Factorization of 914

Prime factors of 914 are 2, 457. Prime factorization of 914 in exponential form is:

914 = 2¹ × 457¹

Step-3: Factors of 896

List of positive integer factors of 896 that divides 896 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448

Step-4: Factors of 914

List of positive integer factors of 914 that divides 896 without a remainder.

1, 2, 457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 896 and 914. The biggest common factor number is the GCF number.
So the greatest common factor 896 and 914 is 2.

Also check out the Least Common Multiple of 896 and 914