What is the Greatest Common Factor of 30544 and 30560?

Greatest common factor (GCF) of 30544 and 30560 is 16.

GCF(30544,30560) = 16

We will now calculate the prime factors of 30544 and 30560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30544 and 30560.

How to find the GCF of 30544 and 30560?

We will first find the prime factorization of 30544 and 30560. After we will calculate the factors of 30544 and 30560 and find the biggest common factor number .

Step-1: Prime Factorization of 30544

Prime factors of 30544 are 2, 23, 83. Prime factorization of 30544 in exponential form is:

30544 = 2⁴ × 23¹ × 83¹

Step-2: 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-3: Factors of 30544

List of positive integer factors of 30544 that divides 30544 without a remainder.

1, 2, 4, 8, 16, 23, 46, 83, 92, 166, 184, 332, 368, 664, 1328, 1909, 3818, 7636, 15272

Step-4: Factors of 30560

List of positive integer factors of 30560 that divides 30544 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30544 and 30560. The biggest common factor number is the GCF number.
So the greatest common factor 30544 and 30560 is 16.

Also check out the Least Common Multiple of 30544 and 30560