What is the Greatest Common Factor of 10647 and 10654?

Greatest common factor (GCF) of 10647 and 10654 is 7.

GCF(10647,10654) = 7

We will now calculate the prime factors of 10647 and 10654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10647 and 10654.

How to find the GCF of 10647 and 10654?

We will first find the prime factorization of 10647 and 10654. After we will calculate the factors of 10647 and 10654 and find the biggest common factor number .

Step-1: Prime Factorization of 10647

Prime factors of 10647 are 3, 7, 13. Prime factorization of 10647 in exponential form is:

10647 = 3² × 7¹ × 13²

Step-2: Prime Factorization of 10654

Prime factors of 10654 are 2, 7, 761. Prime factorization of 10654 in exponential form is:

10654 = 2¹ × 7¹ × 761¹

Step-3: Factors of 10647

List of positive integer factors of 10647 that divides 10647 without a remainder.

1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 169, 273, 507, 819, 1183, 1521, 3549

Step-4: Factors of 10654

List of positive integer factors of 10654 that divides 10647 without a remainder.

1, 2, 7, 14, 761, 1522, 5327

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10647 and 10654. The biggest common factor number is the GCF number.
So the greatest common factor 10647 and 10654 is 7.

Also check out the Least Common Multiple of 10647 and 10654