What is the Greatest Common Factor of 30576 and 30591?

Greatest common factor (GCF) of 30576 and 30591 is 3.

GCF(30576,30591) = 3

We will now calculate the prime factors of 30576 and 30591, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30576 and 30591.

How to find the GCF of 30576 and 30591?

We will first find the prime factorization of 30576 and 30591. After we will calculate the factors of 30576 and 30591 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 30591

Prime factors of 30591 are 3, 11, 103. Prime factorization of 30591 in exponential form is:

30591 = 3³ × 11¹ × 103¹

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 30591

List of positive integer factors of 30591 that divides 30576 without a remainder.

1, 3, 9, 11, 27, 33, 99, 103, 297, 309, 927, 1133, 2781, 3399, 10197

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30576 and 30591. The biggest common factor number is the GCF number.
So the greatest common factor 30576 and 30591 is 3.

Also check out the Least Common Multiple of 30576 and 30591