What is the Greatest Common Factor of 27600 and 27609?

Greatest common factor (GCF) of 27600 and 27609 is 3.

GCF(27600,27609) = 3

We will now calculate the prime factors of 27600 and 27609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27600 and 27609.

How to find the GCF of 27600 and 27609?

We will first find the prime factorization of 27600 and 27609. After we will calculate the factors of 27600 and 27609 and find the biggest common factor number .

Step-1: Prime Factorization of 27600

Prime factors of 27600 are 2, 3, 5, 23. Prime factorization of 27600 in exponential form is:

27600 = 2⁴ × 3¹ × 5² × 23¹

Step-2: Prime Factorization of 27609

Prime factors of 27609 are 3, 9203. Prime factorization of 27609 in exponential form is:

27609 = 3¹ × 9203¹

Step-3: Factors of 27600

List of positive integer factors of 27600 that divides 27600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 23, 24, 25, 30, 40, 46, 48, 50, 60, 69, 75, 80, 92, 100, 115, 120, 138, 150, 184, 200, 230, 240, 276, 300, 345, 368, 400, 460, 552, 575, 600, 690, 920, 1104, 1150, 1200, 1380, 1725, 1840, 2300, 2760, 3450, 4600, 5520, 6900, 9200, 13800

Step-4: Factors of 27609

List of positive integer factors of 27609 that divides 27600 without a remainder.

1, 3, 9203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27600 and 27609. The biggest common factor number is the GCF number.
So the greatest common factor 27600 and 27609 is 3.

Also check out the Least Common Multiple of 27600 and 27609