What is the Greatest Common Factor of 2900 and 2914?

Greatest common factor (GCF) of 2900 and 2914 is 2.

GCF(2900,2914) = 2

We will now calculate the prime factors of 2900 and 2914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2900 and 2914.

How to find the GCF of 2900 and 2914?

We will first find the prime factorization of 2900 and 2914. After we will calculate the factors of 2900 and 2914 and find the biggest common factor number .

Step-1: Prime Factorization of 2900

Prime factors of 2900 are 2, 5, 29. Prime factorization of 2900 in exponential form is:

2900 = 2² × 5² × 29¹

Step-2: Prime Factorization of 2914

Prime factors of 2914 are 2, 31, 47. Prime factorization of 2914 in exponential form is:

2914 = 2¹ × 31¹ × 47¹

Step-3: Factors of 2900

List of positive integer factors of 2900 that divides 2900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 29, 50, 58, 100, 116, 145, 290, 580, 725, 1450

Step-4: Factors of 2914

List of positive integer factors of 2914 that divides 2900 without a remainder.

1, 2, 31, 47, 62, 94, 1457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2900 and 2914. The biggest common factor number is the GCF number.
So the greatest common factor 2900 and 2914 is 2.

Also check out the Least Common Multiple of 2900 and 2914