What is the Greatest Common Factor of 30576 and 30590?

Greatest common factor (GCF) of 30576 and 30590 is 14.

GCF(30576,30590) = 14

We will now calculate the prime factors of 30576 and 30590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30576 and 30590.

How to find the GCF of 30576 and 30590?

We will first find the prime factorization of 30576 and 30590. After we will calculate the factors of 30576 and 30590 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 30590

Prime factors of 30590 are 2, 5, 7, 19, 23. Prime factorization of 30590 in exponential form is:

30590 = 2¹ × 5¹ × 7¹ × 19¹ × 23¹

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 30590

List of positive integer factors of 30590 that divides 30576 without a remainder.

1, 2, 5, 7, 10, 14, 19, 23, 35, 38, 46, 70, 95, 115, 133, 161, 190, 230, 266, 322, 437, 665, 805, 874, 1330, 1610, 2185, 3059, 4370, 6118, 15295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30576 and 30590. The biggest common factor number is the GCF number.
So the greatest common factor 30576 and 30590 is 14.

Also check out the Least Common Multiple of 30576 and 30590