What is the Greatest Common Factor of 53900 and 53914?

Greatest common factor (GCF) of 53900 and 53914 is 14.

GCF(53900,53914) = 14

We will now calculate the prime factors of 53900 and 53914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53900 and 53914.

How to find the GCF of 53900 and 53914?

We will first find the prime factorization of 53900 and 53914. After we will calculate the factors of 53900 and 53914 and find the biggest common factor number .

Step-1: Prime Factorization of 53900

Prime factors of 53900 are 2, 5, 7, 11. Prime factorization of 53900 in exponential form is:

53900 = 2² × 5² × 7² × 11¹

Step-2: Prime Factorization of 53914

Prime factors of 53914 are 2, 7, 3851. Prime factorization of 53914 in exponential form is:

53914 = 2¹ × 7¹ × 3851¹

Step-3: Factors of 53900

List of positive integer factors of 53900 that divides 53900 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 49, 50, 55, 70, 77, 98, 100, 110, 140, 154, 175, 196, 220, 245, 275, 308, 350, 385, 490, 539, 550, 700, 770, 980, 1078, 1100, 1225, 1540, 1925, 2156, 2450, 2695, 3850, 4900, 5390, 7700, 10780, 13475, 26950

Step-4: Factors of 53914

List of positive integer factors of 53914 that divides 53900 without a remainder.

1, 2, 7, 14, 3851, 7702, 26957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53900 and 53914. The biggest common factor number is the GCF number.
So the greatest common factor 53900 and 53914 is 14.

Also check out the Least Common Multiple of 53900 and 53914