What is the Greatest Common Factor of 14889 and 14896?

Greatest common factor (GCF) of 14889 and 14896 is 7.

GCF(14889,14896) = 7

We will now calculate the prime factors of 14889 and 14896, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14889 and 14896.

How to find the GCF of 14889 and 14896?

We will first find the prime factorization of 14889 and 14896. After we will calculate the factors of 14889 and 14896 and find the biggest common factor number .

Step-1: Prime Factorization of 14889

Prime factors of 14889 are 3, 7, 709. Prime factorization of 14889 in exponential form is:

14889 = 3¹ × 7¹ × 709¹

Step-2: 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-3: Factors of 14889

List of positive integer factors of 14889 that divides 14889 without a remainder.

1, 3, 7, 21, 709, 2127, 4963

Step-4: Factors of 14896

List of positive integer factors of 14896 that divides 14889 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14889 and 14896. The biggest common factor number is the GCF number.
So the greatest common factor 14889 and 14896 is 7.

Also check out the Least Common Multiple of 14889 and 14896