What is the Greatest Common Factor of 10688 and 10706?

Greatest common factor (GCF) of 10688 and 10706 is 2.

GCF(10688,10706) = 2

We will now calculate the prime factors of 10688 and 10706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10688 and 10706.

How to find the GCF of 10688 and 10706?

We will first find the prime factorization of 10688 and 10706. After we will calculate the factors of 10688 and 10706 and find the biggest common factor number .

Step-1: Prime Factorization of 10688

Prime factors of 10688 are 2, 167. Prime factorization of 10688 in exponential form is:

10688 = 2⁶ × 167¹

Step-2: Prime Factorization of 10706

Prime factors of 10706 are 2, 53, 101. Prime factorization of 10706 in exponential form is:

10706 = 2¹ × 53¹ × 101¹

Step-3: Factors of 10688

List of positive integer factors of 10688 that divides 10688 without a remainder.

1, 2, 4, 8, 16, 32, 64, 167, 334, 668, 1336, 2672, 5344

Step-4: Factors of 10706

List of positive integer factors of 10706 that divides 10688 without a remainder.

1, 2, 53, 101, 106, 202, 5353

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10688 and 10706. The biggest common factor number is the GCF number.
So the greatest common factor 10688 and 10706 is 2.

Also check out the Least Common Multiple of 10688 and 10706