What is the Greatest Common Factor of 53800 and 53814?

Greatest common factor (GCF) of 53800 and 53814 is 2.

GCF(53800,53814) = 2

We will now calculate the prime factors of 53800 and 53814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53800 and 53814.

How to find the GCF of 53800 and 53814?

We will first find the prime factorization of 53800 and 53814. After we will calculate the factors of 53800 and 53814 and find the biggest common factor number .

Step-1: Prime Factorization of 53800

Prime factors of 53800 are 2, 5, 269. Prime factorization of 53800 in exponential form is:

53800 = 2³ × 5² × 269¹

Step-2: Prime Factorization of 53814

Prime factors of 53814 are 2, 3, 8969. Prime factorization of 53814 in exponential form is:

53814 = 2¹ × 3¹ × 8969¹

Step-3: Factors of 53800

List of positive integer factors of 53800 that divides 53800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 269, 538, 1076, 1345, 2152, 2690, 5380, 6725, 10760, 13450, 26900

Step-4: Factors of 53814

List of positive integer factors of 53814 that divides 53800 without a remainder.

1, 2, 3, 6, 8969, 17938, 26907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53800 and 53814. The biggest common factor number is the GCF number.
So the greatest common factor 53800 and 53814 is 2.

Also check out the Least Common Multiple of 53800 and 53814