What is the Greatest Common Factor of 30560 and 30576?

Greatest common factor (GCF) of 30560 and 30576 is 16.

GCF(30560,30576) = 16

We will now calculate the prime factors of 30560 and 30576, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30560 and 30576.

How to find the GCF of 30560 and 30576?

We will first find the prime factorization of 30560 and 30576. After we will calculate the factors of 30560 and 30576 and find the biggest common factor number .

Step-1: Prime Factorization of 30560

Prime factors of 30560 are 2, 5, 191. Prime factorization of 30560 in exponential form is:

30560 = 2⁵ × 5¹ × 191¹

Step-2: 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-3: Factors of 30560

List of positive integer factors of 30560 that divides 30560 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 191, 382, 764, 955, 1528, 1910, 3056, 3820, 6112, 7640, 15280

Step-4: Factors of 30576

List of positive integer factors of 30576 that divides 30560 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30560 and 30576. The biggest common factor number is the GCF number.
So the greatest common factor 30560 and 30576 is 16.

Also check out the Least Common Multiple of 30560 and 30576