What is the Greatest Common Factor of 30576 and 30586?

Greatest common factor (GCF) of 30576 and 30586 is 2.

GCF(30576,30586) = 2

We will now calculate the prime factors of 30576 and 30586, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30576 and 30586.

How to find the GCF of 30576 and 30586?

We will first find the prime factorization of 30576 and 30586. After we will calculate the factors of 30576 and 30586 and find the biggest common factor number .

Step-1: Prime Factorization of 30576

Prime factors of 30576 are 2, 3, 7, 13. Prime factorization of 30576 in exponential form is:

30576 = 2⁴ × 3¹ × 7² × 13¹

Step-2: 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-3: Factors of 30576

List of positive integer factors of 30576 that divides 30576 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 39, 42, 48, 49, 52, 56, 78, 84, 91, 98, 104, 112, 147, 156, 168, 182, 196, 208, 273, 294, 312, 336, 364, 392, 546, 588, 624, 637, 728, 784, 1092, 1176, 1274, 1456, 1911, 2184, 2352, 2548, 3822, 4368, 5096, 7644, 10192, 15288

Step-4: Factors of 30586

List of positive integer factors of 30586 that divides 30576 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30576 and 30586. The biggest common factor number is the GCF number.
So the greatest common factor 30576 and 30586 is 2.

Also check out the Least Common Multiple of 30576 and 30586