What is the Greatest Common Factor of 27684 and 27702?

Greatest common factor (GCF) of 27684 and 27702 is 18.

GCF(27684,27702) = 18

We will now calculate the prime factors of 27684 and 27702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27684 and 27702.

How to find the GCF of 27684 and 27702?

We will first find the prime factorization of 27684 and 27702. After we will calculate the factors of 27684 and 27702 and find the biggest common factor number .

Step-1: Prime Factorization of 27684

Prime factors of 27684 are 2, 3, 769. Prime factorization of 27684 in exponential form is:

27684 = 2² × 3² × 769¹

Step-2: Prime Factorization of 27702

Prime factors of 27702 are 2, 3, 19. Prime factorization of 27702 in exponential form is:

27702 = 2¹ × 3⁶ × 19¹

Step-3: Factors of 27684

List of positive integer factors of 27684 that divides 27684 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 769, 1538, 2307, 3076, 4614, 6921, 9228, 13842

Step-4: Factors of 27702

List of positive integer factors of 27702 that divides 27684 without a remainder.

1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 243, 342, 486, 513, 729, 1026, 1458, 1539, 3078, 4617, 9234, 13851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27684 and 27702. The biggest common factor number is the GCF number.
So the greatest common factor 27684 and 27702 is 18.

Also check out the Least Common Multiple of 27684 and 27702