What is the Greatest Common Factor of 27683 and 27702?

Greatest common factor (GCF) of 27683 and 27702 is 19.

GCF(27683,27702) = 19

We will now calculate the prime factors of 27683 and 27702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27683 and 27702.

How to find the GCF of 27683 and 27702?

We will first find the prime factorization of 27683 and 27702. After we will calculate the factors of 27683 and 27702 and find the biggest common factor number .

Step-1: Prime Factorization of 27683

Prime factors of 27683 are 19, 31, 47. Prime factorization of 27683 in exponential form is:

27683 = 19¹ × 31¹ × 47¹

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 27683

List of positive integer factors of 27683 that divides 27683 without a remainder.

1, 19, 31, 47, 589, 893, 1457

Step-4: Factors of 27702

List of positive integer factors of 27702 that divides 27683 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 27683 and 27702. The biggest common factor number is the GCF number.
So the greatest common factor 27683 and 27702 is 19.

Also check out the Least Common Multiple of 27683 and 27702