What is the Greatest Common Factor of 10659 and 10678?

Greatest common factor (GCF) of 10659 and 10678 is 19.

GCF(10659,10678) = 19

We will now calculate the prime factors of 10659 and 10678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10659 and 10678.

How to find the GCF of 10659 and 10678?

We will first find the prime factorization of 10659 and 10678. After we will calculate the factors of 10659 and 10678 and find the biggest common factor number .

Step-1: Prime Factorization of 10659

Prime factors of 10659 are 3, 11, 17, 19. Prime factorization of 10659 in exponential form is:

10659 = 3¹ × 11¹ × 17¹ × 19¹

Step-2: Prime Factorization of 10678

Prime factors of 10678 are 2, 19, 281. Prime factorization of 10678 in exponential form is:

10678 = 2¹ × 19¹ × 281¹

Step-3: Factors of 10659

List of positive integer factors of 10659 that divides 10659 without a remainder.

1, 3, 11, 17, 19, 33, 51, 57, 187, 209, 323, 561, 627, 969, 3553

Step-4: Factors of 10678

List of positive integer factors of 10678 that divides 10659 without a remainder.

1, 2, 19, 38, 281, 562, 5339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10659 and 10678. The biggest common factor number is the GCF number.
So the greatest common factor 10659 and 10678 is 19.

Also check out the Least Common Multiple of 10659 and 10678