What is the Greatest Common Factor of 10674 and 10686?

Greatest common factor (GCF) of 10674 and 10686 is 6.

GCF(10674,10686) = 6

We will now calculate the prime factors of 10674 and 10686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10674 and 10686.

How to find the GCF of 10674 and 10686?

We will first find the prime factorization of 10674 and 10686. After we will calculate the factors of 10674 and 10686 and find the biggest common factor number .

Step-1: Prime Factorization of 10674

Prime factors of 10674 are 2, 3, 593. Prime factorization of 10674 in exponential form is:

10674 = 2¹ × 3² × 593¹

Step-2: Prime Factorization of 10686

Prime factors of 10686 are 2, 3, 13, 137. Prime factorization of 10686 in exponential form is:

10686 = 2¹ × 3¹ × 13¹ × 137¹

Step-3: Factors of 10674

List of positive integer factors of 10674 that divides 10674 without a remainder.

1, 2, 3, 6, 9, 18, 593, 1186, 1779, 3558, 5337

Step-4: Factors of 10686

List of positive integer factors of 10686 that divides 10674 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 137, 274, 411, 822, 1781, 3562, 5343

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10674 and 10686. The biggest common factor number is the GCF number.
So the greatest common factor 10674 and 10686 is 6.

Also check out the Least Common Multiple of 10674 and 10686