What is the Greatest Common Factor of 10686 and 10700?

Greatest common factor (GCF) of 10686 and 10700 is 2.

GCF(10686,10700) = 2

We will now calculate the prime factors of 10686 and 10700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10686 and 10700.

How to find the GCF of 10686 and 10700?

We will first find the prime factorization of 10686 and 10700. After we will calculate the factors of 10686 and 10700 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 10700

Prime factors of 10700 are 2, 5, 107. Prime factorization of 10700 in exponential form is:

10700 = 2² × 5² × 107¹

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 10700

List of positive integer factors of 10700 that divides 10686 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 107, 214, 428, 535, 1070, 2140, 2675, 5350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10686 and 10700. The biggest common factor number is the GCF number.
So the greatest common factor 10686 and 10700 is 2.

Also check out the Least Common Multiple of 10686 and 10700