What is the Greatest Common Factor of 27642 and 27657?

Greatest common factor (GCF) of 27642 and 27657 is 3.

GCF(27642,27657) = 3

We will now calculate the prime factors of 27642 and 27657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27642 and 27657.

How to find the GCF of 27642 and 27657?

We will first find the prime factorization of 27642 and 27657. After we will calculate the factors of 27642 and 27657 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 27657

Prime factors of 27657 are 3, 7, 439. Prime factorization of 27657 in exponential form is:

27657 = 3² × 7¹ × 439¹

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 27657

List of positive integer factors of 27657 that divides 27642 without a remainder.

1, 3, 7, 9, 21, 63, 439, 1317, 3073, 3951, 9219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27642 and 27657. The biggest common factor number is the GCF number.
So the greatest common factor 27642 and 27657 is 3.

Also check out the Least Common Multiple of 27642 and 27657