What is the Greatest Common Factor of 14896 and 14914?

Greatest common factor (GCF) of 14896 and 14914 is 2.

GCF(14896,14914) = 2

We will now calculate the prime factors of 14896 and 14914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14896 and 14914.

How to find the GCF of 14896 and 14914?

We will first find the prime factorization of 14896 and 14914. After we will calculate the factors of 14896 and 14914 and find the biggest common factor number .

Step-1: Prime Factorization of 14896

Prime factors of 14896 are 2, 7, 19. Prime factorization of 14896 in exponential form is:

14896 = 2⁴ × 7² × 19¹

Step-2: Prime Factorization of 14914

Prime factors of 14914 are 2, 7457. Prime factorization of 14914 in exponential form is:

14914 = 2¹ × 7457¹

Step-3: Factors of 14896

List of positive integer factors of 14896 that divides 14896 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 49, 56, 76, 98, 112, 133, 152, 196, 266, 304, 392, 532, 784, 931, 1064, 1862, 2128, 3724, 7448

Step-4: Factors of 14914

List of positive integer factors of 14914 that divides 14896 without a remainder.

1, 2, 7457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14896 and 14914. The biggest common factor number is the GCF number.
So the greatest common factor 14896 and 14914 is 2.

Also check out the Least Common Multiple of 14896 and 14914