What is the Greatest Common Factor of 27586 and 27600?

Greatest common factor (GCF) of 27586 and 27600 is 2.

GCF(27586,27600) = 2

We will now calculate the prime factors of 27586 and 27600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27586 and 27600.

How to find the GCF of 27586 and 27600?

We will first find the prime factorization of 27586 and 27600. After we will calculate the factors of 27586 and 27600 and find the biggest common factor number .

Step-1: Prime Factorization of 27586

Prime factors of 27586 are 2, 13, 1061. Prime factorization of 27586 in exponential form is:

27586 = 2¹ × 13¹ × 1061¹

Step-2: 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-3: Factors of 27586

List of positive integer factors of 27586 that divides 27586 without a remainder.

1, 2, 13, 26, 1061, 2122, 13793

Step-4: Factors of 27600

List of positive integer factors of 27600 that divides 27586 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27586 and 27600. The biggest common factor number is the GCF number.
So the greatest common factor 27586 and 27600 is 2.

Also check out the Least Common Multiple of 27586 and 27600