What is the Greatest Common Factor of 13750 and 13770?

Greatest common factor (GCF) of 13750 and 13770 is 10.

GCF(13750,13770) = 10

We will now calculate the prime factors of 13750 and 13770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13750 and 13770.

How to find the GCF of 13750 and 13770?

We will first find the prime factorization of 13750 and 13770. After we will calculate the factors of 13750 and 13770 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13770

Prime factors of 13770 are 2, 3, 5, 17. Prime factorization of 13770 in exponential form is:

13770 = 2¹ × 3⁴ × 5¹ × 17¹

Step-3: Factors of 13750

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

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

Step-4: Factors of 13770

List of positive integer factors of 13770 that divides 13750 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54, 81, 85, 90, 102, 135, 153, 162, 170, 255, 270, 306, 405, 459, 510, 765, 810, 918, 1377, 1530, 2295, 2754, 4590, 6885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13750 and 13770. The biggest common factor number is the GCF number.
So the greatest common factor 13750 and 13770 is 10.

Also check out the Least Common Multiple of 13750 and 13770