What is the Greatest Common Factor of 13742 and 13758?

Greatest common factor (GCF) of 13742 and 13758 is 2.

GCF(13742,13758) = 2

We will now calculate the prime factors of 13742 and 13758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13742 and 13758.

How to find the GCF of 13742 and 13758?

We will first find the prime factorization of 13742 and 13758. After we will calculate the factors of 13742 and 13758 and find the biggest common factor number .

Step-1: Prime Factorization of 13742

Prime factors of 13742 are 2, 6871. Prime factorization of 13742 in exponential form is:

13742 = 2¹ × 6871¹

Step-2: Prime Factorization of 13758

Prime factors of 13758 are 2, 3, 2293. Prime factorization of 13758 in exponential form is:

13758 = 2¹ × 3¹ × 2293¹

Step-3: Factors of 13742

List of positive integer factors of 13742 that divides 13742 without a remainder.

1, 2, 6871

Step-4: Factors of 13758

List of positive integer factors of 13758 that divides 13742 without a remainder.

1, 2, 3, 6, 2293, 4586, 6879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13742 and 13758. The biggest common factor number is the GCF number.
So the greatest common factor 13742 and 13758 is 2.

Also check out the Least Common Multiple of 13742 and 13758