What is the Greatest Common Factor of 13730 and 13750?

Greatest common factor (GCF) of 13730 and 13750 is 10.

GCF(13730,13750) = 10

We will now calculate the prime factors of 13730 and 13750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13730 and 13750.

How to find the GCF of 13730 and 13750?

We will first find the prime factorization of 13730 and 13750. After we will calculate the factors of 13730 and 13750 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13750

Prime factors of 13750 are 2, 5, 11. Prime factorization of 13750 in exponential form is:

13750 = 2¹ × 5⁴ × 11¹

Step-3: Factors of 13730

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

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

Step-4: Factors of 13750

List of positive integer factors of 13750 that divides 13730 without a remainder.

1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 125, 250, 275, 550, 625, 1250, 1375, 2750, 6875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13730 and 13750. The biggest common factor number is the GCF number.
So the greatest common factor 13730 and 13750 is 10.

Also check out the Least Common Multiple of 13730 and 13750