What is the Greatest Common Factor of 13746 and 13760?

Greatest common factor (GCF) of 13746 and 13760 is 2.

GCF(13746,13760) = 2

We will now calculate the prime factors of 13746 and 13760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13746 and 13760.

How to find the GCF of 13746 and 13760?

We will first find the prime factorization of 13746 and 13760. After we will calculate the factors of 13746 and 13760 and find the biggest common factor number .

Step-1: Prime Factorization of 13746

Prime factors of 13746 are 2, 3, 29, 79. Prime factorization of 13746 in exponential form is:

13746 = 2¹ × 3¹ × 29¹ × 79¹

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 13746

List of positive integer factors of 13746 that divides 13746 without a remainder.

1, 2, 3, 6, 29, 58, 79, 87, 158, 174, 237, 474, 2291, 4582, 6873

Step-4: Factors of 13760

List of positive integer factors of 13760 that divides 13746 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 13746 and 13760. The biggest common factor number is the GCF number.
So the greatest common factor 13746 and 13760 is 2.

Also check out the Least Common Multiple of 13746 and 13760