What is the Greatest Common Factor of 27674 and 27678?

Greatest common factor (GCF) of 27674 and 27678 is 2.

GCF(27674,27678) = 2

We will now calculate the prime factors of 27674 and 27678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27674 and 27678.

How to find the GCF of 27674 and 27678?

We will first find the prime factorization of 27674 and 27678. After we will calculate the factors of 27674 and 27678 and find the biggest common factor number .

Step-1: Prime Factorization of 27674

Prime factors of 27674 are 2, 101, 137. Prime factorization of 27674 in exponential form is:

27674 = 2¹ × 101¹ × 137¹

Step-2: Prime Factorization of 27678

Prime factors of 27678 are 2, 3, 7, 659. Prime factorization of 27678 in exponential form is:

27678 = 2¹ × 3¹ × 7¹ × 659¹

Step-3: Factors of 27674

List of positive integer factors of 27674 that divides 27674 without a remainder.

1, 2, 101, 137, 202, 274, 13837

Step-4: Factors of 27678

List of positive integer factors of 27678 that divides 27674 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 659, 1318, 1977, 3954, 4613, 9226, 13839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27674 and 27678. The biggest common factor number is the GCF number.
So the greatest common factor 27674 and 27678 is 2.

Also check out the Least Common Multiple of 27674 and 27678