What is the Greatest Common Factor of 27324 and 27342?

Greatest common factor (GCF) of 27324 and 27342 is 18.

GCF(27324,27342) = 18

We will now calculate the prime factors of 27324 and 27342, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27324 and 27342.

How to find the GCF of 27324 and 27342?

We will first find the prime factorization of 27324 and 27342. After we will calculate the factors of 27324 and 27342 and find the biggest common factor number .

Step-1: Prime Factorization of 27324

Prime factors of 27324 are 2, 3, 11, 23. Prime factorization of 27324 in exponential form is:

27324 = 2² × 3³ × 11¹ × 23¹

Step-2: Prime Factorization of 27342

Prime factors of 27342 are 2, 3, 7, 31. Prime factorization of 27342 in exponential form is:

27342 = 2¹ × 3² × 7² × 31¹

Step-3: Factors of 27324

List of positive integer factors of 27324 that divides 27324 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 23, 27, 33, 36, 44, 46, 54, 66, 69, 92, 99, 108, 132, 138, 198, 207, 253, 276, 297, 396, 414, 506, 594, 621, 759, 828, 1012, 1188, 1242, 1518, 2277, 2484, 3036, 4554, 6831, 9108, 13662

Step-4: Factors of 27342

List of positive integer factors of 27342 that divides 27324 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 31, 42, 49, 62, 63, 93, 98, 126, 147, 186, 217, 279, 294, 434, 441, 558, 651, 882, 1302, 1519, 1953, 3038, 3906, 4557, 9114, 13671

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27324 and 27342. The biggest common factor number is the GCF number.
So the greatest common factor 27324 and 27342 is 18.

Also check out the Least Common Multiple of 27324 and 27342