What is the Greatest Common Factor of 10689 and 10700?

Greatest common factor (GCF) of 10689 and 10700 is 1.

GCF(10689,10700) = 1

We will now calculate the prime factors of 10689 and 10700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10689 and 10700.

How to find the GCF of 10689 and 10700?

We will first find the prime factorization of 10689 and 10700. After we will calculate the factors of 10689 and 10700 and find the biggest common factor number .

Step-1: Prime Factorization of 10689

Prime factors of 10689 are 3, 7, 509. Prime factorization of 10689 in exponential form is:

10689 = 3¹ × 7¹ × 509¹

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 10689

List of positive integer factors of 10689 that divides 10689 without a remainder.

1, 3, 7, 21, 509, 1527, 3563

Step-4: Factors of 10700

List of positive integer factors of 10700 that divides 10689 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 10689 and 10700. The biggest common factor number is the GCF number.
So the greatest common factor 10689 and 10700 is 1.

Also check out the Least Common Multiple of 10689 and 10700