What is the Greatest Common Factor of 13754 and 13768?

Greatest common factor (GCF) of 13754 and 13768 is 2.

GCF(13754,13768) = 2

We will now calculate the prime factors of 13754 and 13768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13754 and 13768.

How to find the GCF of 13754 and 13768?

We will first find the prime factorization of 13754 and 13768. After we will calculate the factors of 13754 and 13768 and find the biggest common factor number .

Step-1: Prime Factorization of 13754

Prime factors of 13754 are 2, 13, 23. Prime factorization of 13754 in exponential form is:

13754 = 2¹ × 13¹ × 23²

Step-2: Prime Factorization of 13768

Prime factors of 13768 are 2, 1721. Prime factorization of 13768 in exponential form is:

13768 = 2³ × 1721¹

Step-3: Factors of 13754

List of positive integer factors of 13754 that divides 13754 without a remainder.

1, 2, 13, 23, 26, 46, 299, 529, 598, 1058, 6877

Step-4: Factors of 13768

List of positive integer factors of 13768 that divides 13754 without a remainder.

1, 2, 4, 8, 1721, 3442, 6884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13754 and 13768. The biggest common factor number is the GCF number.
So the greatest common factor 13754 and 13768 is 2.

Also check out the Least Common Multiple of 13754 and 13768