What is the Greatest Common Factor of 30586 and 30600?

Greatest common factor (GCF) of 30586 and 30600 is 2.

GCF(30586,30600) = 2

We will now calculate the prime factors of 30586 and 30600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30586 and 30600.

How to find the GCF of 30586 and 30600?

We will first find the prime factorization of 30586 and 30600. After we will calculate the factors of 30586 and 30600 and find the biggest common factor number .

Step-1: Prime Factorization of 30586

Prime factors of 30586 are 2, 41, 373. Prime factorization of 30586 in exponential form is:

30586 = 2¹ × 41¹ × 373¹

Step-2: Prime Factorization of 30600

Prime factors of 30600 are 2, 3, 5, 17. Prime factorization of 30600 in exponential form is:

30600 = 2³ × 3² × 5² × 17¹

Step-3: Factors of 30586

List of positive integer factors of 30586 that divides 30586 without a remainder.

1, 2, 41, 82, 373, 746, 15293

Step-4: Factors of 30600

List of positive integer factors of 30600 that divides 30586 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 20, 24, 25, 30, 34, 36, 40, 45, 50, 51, 60, 68, 72, 75, 85, 90, 100, 102, 120, 136, 150, 153, 170, 180, 200, 204, 225, 255, 300, 306, 340, 360, 408, 425, 450, 510, 600, 612, 680, 765, 850, 900, 1020, 1224, 1275, 1530, 1700, 1800, 2040, 2550, 3060, 3400, 3825, 5100, 6120, 7650, 10200, 15300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30586 and 30600. The biggest common factor number is the GCF number.
So the greatest common factor 30586 and 30600 is 2.

Also check out the Least Common Multiple of 30586 and 30600