What is the Greatest Common Factor of 13760 and 13778?

Greatest common factor (GCF) of 13760 and 13778 is 2.

GCF(13760,13778) = 2

We will now calculate the prime factors of 13760 and 13778, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13760 and 13778.

How to find the GCF of 13760 and 13778?

We will first find the prime factorization of 13760 and 13778. After we will calculate the factors of 13760 and 13778 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13778

Prime factors of 13778 are 2, 83. Prime factorization of 13778 in exponential form is:

13778 = 2¹ × 83²

Step-3: Factors of 13760

List of positive integer factors of 13760 that divides 13760 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

Step-4: Factors of 13778

List of positive integer factors of 13778 that divides 13760 without a remainder.

1, 2, 83, 166, 6889

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13760 and 13778. The biggest common factor number is the GCF number.
So the greatest common factor 13760 and 13778 is 2.

Also check out the Least Common Multiple of 13760 and 13778