What is the Greatest Common Factor of 27105 and 27120?

Greatest common factor (GCF) of 27105 and 27120 is 15.

GCF(27105,27120) = 15

We will now calculate the prime factors of 27105 and 27120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27105 and 27120.

How to find the GCF of 27105 and 27120?

We will first find the prime factorization of 27105 and 27120. After we will calculate the factors of 27105 and 27120 and find the biggest common factor number .

Step-1: Prime Factorization of 27105

Prime factors of 27105 are 3, 5, 13, 139. Prime factorization of 27105 in exponential form is:

27105 = 3¹ × 5¹ × 13¹ × 139¹

Step-2: Prime Factorization of 27120

Prime factors of 27120 are 2, 3, 5, 113. Prime factorization of 27120 in exponential form is:

27120 = 2⁴ × 3¹ × 5¹ × 113¹

Step-3: Factors of 27105

List of positive integer factors of 27105 that divides 27105 without a remainder.

1, 3, 5, 13, 15, 39, 65, 139, 195, 417, 695, 1807, 2085, 5421, 9035

Step-4: Factors of 27120

List of positive integer factors of 27120 that divides 27105 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 113, 120, 226, 240, 339, 452, 565, 678, 904, 1130, 1356, 1695, 1808, 2260, 2712, 3390, 4520, 5424, 6780, 9040, 13560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27105 and 27120. The biggest common factor number is the GCF number.
So the greatest common factor 27105 and 27120 is 15.

Also check out the Least Common Multiple of 27105 and 27120