What is the Greatest Common Factor of 30540 and 30560?

Greatest common factor (GCF) of 30540 and 30560 is 20.

GCF(30540,30560) = 20

We will now calculate the prime factors of 30540 and 30560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30540 and 30560.

How to find the GCF of 30540 and 30560?

We will first find the prime factorization of 30540 and 30560. After we will calculate the factors of 30540 and 30560 and find the biggest common factor number .

Step-1: Prime Factorization of 30540

Prime factors of 30540 are 2, 3, 5, 509. Prime factorization of 30540 in exponential form is:

30540 = 2² × 3¹ × 5¹ × 509¹

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 30540

List of positive integer factors of 30540 that divides 30540 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 509, 1018, 1527, 2036, 2545, 3054, 5090, 6108, 7635, 10180, 15270

Step-4: Factors of 30560

List of positive integer factors of 30560 that divides 30540 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 30540 and 30560. The biggest common factor number is the GCF number.
So the greatest common factor 30540 and 30560 is 20.

Also check out the Least Common Multiple of 30540 and 30560