What is the Greatest Common Factor of 27625 and 27642?

Greatest common factor (GCF) of 27625 and 27642 is 17.

GCF(27625,27642) = 17

We will now calculate the prime factors of 27625 and 27642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27625 and 27642.

How to find the GCF of 27625 and 27642?

We will first find the prime factorization of 27625 and 27642. After we will calculate the factors of 27625 and 27642 and find the biggest common factor number .

Step-1: Prime Factorization of 27625

Prime factors of 27625 are 5, 13, 17. Prime factorization of 27625 in exponential form is:

27625 = 5³ × 13¹ × 17¹

Step-2: 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-3: Factors of 27625

List of positive integer factors of 27625 that divides 27625 without a remainder.

1, 5, 13, 17, 25, 65, 85, 125, 221, 325, 425, 1105, 1625, 2125, 5525

Step-4: Factors of 27642

List of positive integer factors of 27642 that divides 27625 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27625 and 27642. The biggest common factor number is the GCF number.
So the greatest common factor 27625 and 27642 is 17.

Also check out the Least Common Multiple of 27625 and 27642