What is the Greatest Common Factor of 10686 and 10704?

Greatest common factor (GCF) of 10686 and 10704 is 6.

GCF(10686,10704) = 6

We will now calculate the prime factors of 10686 and 10704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10686 and 10704.

How to find the GCF of 10686 and 10704?

We will first find the prime factorization of 10686 and 10704. After we will calculate the factors of 10686 and 10704 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10704

Prime factors of 10704 are 2, 3, 223. Prime factorization of 10704 in exponential form is:

10704 = 2⁴ × 3¹ × 223¹

Step-3: Factors of 10686

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

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

Step-4: Factors of 10704

List of positive integer factors of 10704 that divides 10686 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 223, 446, 669, 892, 1338, 1784, 2676, 3568, 5352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10686 and 10704. The biggest common factor number is the GCF number.
So the greatest common factor 10686 and 10704 is 6.

Also check out the Least Common Multiple of 10686 and 10704