What is the Greatest Common Factor of 13740 and 13760?

Greatest common factor (GCF) of 13740 and 13760 is 20.

GCF(13740,13760) = 20

We will now calculate the prime factors of 13740 and 13760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13740 and 13760.

How to find the GCF of 13740 and 13760?

We will first find the prime factorization of 13740 and 13760. After we will calculate the factors of 13740 and 13760 and find the biggest common factor number .

Step-1: Prime Factorization of 13740

Prime factors of 13740 are 2, 3, 5, 229. Prime factorization of 13740 in exponential form is:

13740 = 2² × 3¹ × 5¹ × 229¹

Step-2: Prime Factorization of 13760

Prime factors of 13760 are 2, 5, 43. Prime factorization of 13760 in exponential form is:

13760 = 2⁶ × 5¹ × 43¹

Step-3: Factors of 13740

List of positive integer factors of 13740 that divides 13740 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 229, 458, 687, 916, 1145, 1374, 2290, 2748, 3435, 4580, 6870

Step-4: Factors of 13760

List of positive integer factors of 13760 that divides 13740 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 43, 64, 80, 86, 160, 172, 215, 320, 344, 430, 688, 860, 1376, 1720, 2752, 3440, 6880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13740 and 13760. The biggest common factor number is the GCF number.
So the greatest common factor 13740 and 13760 is 20.

Also check out the Least Common Multiple of 13740 and 13760