What is the Greatest Common Factor of 30576 and 30583?

Greatest common factor (GCF) of 30576 and 30583 is 7.

GCF(30576,30583) = 7

We will now calculate the prime factors of 30576 and 30583, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30576 and 30583.

How to find the GCF of 30576 and 30583?

We will first find the prime factorization of 30576 and 30583. After we will calculate the factors of 30576 and 30583 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 30583

Prime factors of 30583 are 7, 17, 257. Prime factorization of 30583 in exponential form is:

30583 = 7¹ × 17¹ × 257¹

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 30583

List of positive integer factors of 30583 that divides 30576 without a remainder.

1, 7, 17, 119, 257, 1799, 4369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30576 and 30583. The biggest common factor number is the GCF number.
So the greatest common factor 30576 and 30583 is 7.

Also check out the Least Common Multiple of 30576 and 30583