What is the Greatest Common Factor of 49900 and 49914?

Greatest common factor (GCF) of 49900 and 49914 is 2.

GCF(49900,49914) = 2

We will now calculate the prime factors of 49900 and 49914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49900 and 49914.

How to find the GCF of 49900 and 49914?

We will first find the prime factorization of 49900 and 49914. After we will calculate the factors of 49900 and 49914 and find the biggest common factor number .

Step-1: Prime Factorization of 49900

Prime factors of 49900 are 2, 5, 499. Prime factorization of 49900 in exponential form is:

49900 = 2² × 5² × 499¹

Step-2: Prime Factorization of 49914

Prime factors of 49914 are 2, 3, 47, 59. Prime factorization of 49914 in exponential form is:

49914 = 2¹ × 3² × 47¹ × 59¹

Step-3: Factors of 49900

List of positive integer factors of 49900 that divides 49900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 499, 998, 1996, 2495, 4990, 9980, 12475, 24950

Step-4: Factors of 49914

List of positive integer factors of 49914 that divides 49900 without a remainder.

1, 2, 3, 6, 9, 18, 47, 59, 94, 118, 141, 177, 282, 354, 423, 531, 846, 1062, 2773, 5546, 8319, 16638, 24957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49900 and 49914. The biggest common factor number is the GCF number.
So the greatest common factor 49900 and 49914 is 2.

Also check out the Least Common Multiple of 49900 and 49914