What is the Greatest Common Factor of 13710 and 13730?

Greatest common factor (GCF) of 13710 and 13730 is 10.

GCF(13710,13730) = 10

We will now calculate the prime factors of 13710 and 13730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13710 and 13730.

How to find the GCF of 13710 and 13730?

We will first find the prime factorization of 13710 and 13730. After we will calculate the factors of 13710 and 13730 and find the biggest common factor number .

Step-1: Prime Factorization of 13710

Prime factors of 13710 are 2, 3, 5, 457. Prime factorization of 13710 in exponential form is:

13710 = 2¹ × 3¹ × 5¹ × 457¹

Step-2: Prime Factorization of 13730

Prime factors of 13730 are 2, 5, 1373. Prime factorization of 13730 in exponential form is:

13730 = 2¹ × 5¹ × 1373¹

Step-3: Factors of 13710

List of positive integer factors of 13710 that divides 13710 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 457, 914, 1371, 2285, 2742, 4570, 6855

Step-4: Factors of 13730

List of positive integer factors of 13730 that divides 13710 without a remainder.

1, 2, 5, 10, 1373, 2746, 6865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13710 and 13730. The biggest common factor number is the GCF number.
So the greatest common factor 13710 and 13730 is 10.

Also check out the Least Common Multiple of 13710 and 13730