What is the Greatest Common Factor of 6725 and 6734?

Greatest common factor (GCF) of 6725 and 6734 is 1.

GCF(6725,6734) = 1

We will now calculate the prime factors of 6725 and 6734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6725 and 6734.

How to find the GCF of 6725 and 6734?

We will first find the prime factorization of 6725 and 6734. After we will calculate the factors of 6725 and 6734 and find the biggest common factor number .

Step-1: Prime Factorization of 6725

Prime factors of 6725 are 5, 269. Prime factorization of 6725 in exponential form is:

6725 = 5² × 269¹

Step-2: Prime Factorization of 6734

Prime factors of 6734 are 2, 7, 13, 37. Prime factorization of 6734 in exponential form is:

6734 = 2¹ × 7¹ × 13¹ × 37¹

Step-3: Factors of 6725

List of positive integer factors of 6725 that divides 6725 without a remainder.

1, 5, 25, 269, 1345

Step-4: Factors of 6734

List of positive integer factors of 6734 that divides 6725 without a remainder.

1, 2, 7, 13, 14, 26, 37, 74, 91, 182, 259, 481, 518, 962, 3367

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6725 and 6734. The biggest common factor number is the GCF number.
So the greatest common factor 6725 and 6734 is 1.

Also check out the Least Common Multiple of 6725 and 6734