What is the Greatest Common Factor of 13890 and 13900?

Greatest common factor (GCF) of 13890 and 13900 is 10.

GCF(13890,13900) = 10

We will now calculate the prime factors of 13890 and 13900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13890 and 13900.

How to find the GCF of 13890 and 13900?

We will first find the prime factorization of 13890 and 13900. After we will calculate the factors of 13890 and 13900 and find the biggest common factor number .

Step-1: Prime Factorization of 13890

Prime factors of 13890 are 2, 3, 5, 463. Prime factorization of 13890 in exponential form is:

13890 = 2¹ × 3¹ × 5¹ × 463¹

Step-2: Prime Factorization of 13900

Prime factors of 13900 are 2, 5, 139. Prime factorization of 13900 in exponential form is:

13900 = 2² × 5² × 139¹

Step-3: Factors of 13890

List of positive integer factors of 13890 that divides 13890 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 463, 926, 1389, 2315, 2778, 4630, 6945

Step-4: Factors of 13900

List of positive integer factors of 13900 that divides 13890 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 139, 278, 556, 695, 1390, 2780, 3475, 6950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13890 and 13900. The biggest common factor number is the GCF number.
So the greatest common factor 13890 and 13900 is 10.

Also check out the Least Common Multiple of 13890 and 13900