What is the Greatest Common Factor of 4900 and 4914?

Greatest common factor (GCF) of 4900 and 4914 is 14.

GCF(4900,4914) = 14

We will now calculate the prime factors of 4900 and 4914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4900 and 4914.

How to find the GCF of 4900 and 4914?

We will first find the prime factorization of 4900 and 4914. After we will calculate the factors of 4900 and 4914 and find the biggest common factor number .

Step-1: Prime Factorization of 4900

Prime factors of 4900 are 2, 5, 7. Prime factorization of 4900 in exponential form is:

4900 = 2² × 5² × 7²

Step-2: Prime Factorization of 4914

Prime factors of 4914 are 2, 3, 7, 13. Prime factorization of 4914 in exponential form is:

4914 = 2¹ × 3³ × 7¹ × 13¹

Step-3: Factors of 4900

List of positive integer factors of 4900 that divides 4900 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450

Step-4: Factors of 4914

List of positive integer factors of 4914 that divides 4900 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 91, 117, 126, 182, 189, 234, 273, 351, 378, 546, 702, 819, 1638, 2457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4900 and 4914. The biggest common factor number is the GCF number.
So the greatest common factor 4900 and 4914 is 14.

Also check out the Least Common Multiple of 4900 and 4914