What is the Greatest Common Factor of 27642 and 27654?

Greatest common factor (GCF) of 27642 and 27654 is 6.

GCF(27642,27654) = 6

We will now calculate the prime factors of 27642 and 27654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27642 and 27654.

How to find the GCF of 27642 and 27654?

We will first find the prime factorization of 27642 and 27654. After we will calculate the factors of 27642 and 27654 and find the biggest common factor number .

Step-1: Prime Factorization of 27642

Prime factors of 27642 are 2, 3, 17, 271. Prime factorization of 27642 in exponential form is:

27642 = 2¹ × 3¹ × 17¹ × 271¹

Step-2: Prime Factorization of 27654

Prime factors of 27654 are 2, 3, 11, 419. Prime factorization of 27654 in exponential form is:

27654 = 2¹ × 3¹ × 11¹ × 419¹

Step-3: Factors of 27642

List of positive integer factors of 27642 that divides 27642 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 271, 542, 813, 1626, 4607, 9214, 13821

Step-4: Factors of 27654

List of positive integer factors of 27654 that divides 27642 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 419, 838, 1257, 2514, 4609, 9218, 13827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27642 and 27654. The biggest common factor number is the GCF number.
So the greatest common factor 27642 and 27654 is 6.

Also check out the Least Common Multiple of 27642 and 27654