What is the Greatest Common Factor of 30504 and 30510?

Greatest common factor (GCF) of 30504 and 30510 is 6.

GCF(30504,30510) = 6

We will now calculate the prime factors of 30504 and 30510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30504 and 30510.

How to find the GCF of 30504 and 30510?

We will first find the prime factorization of 30504 and 30510. After we will calculate the factors of 30504 and 30510 and find the biggest common factor number .

Step-1: Prime Factorization of 30504

Prime factors of 30504 are 2, 3, 31, 41. Prime factorization of 30504 in exponential form is:

30504 = 2³ × 3¹ × 31¹ × 41¹

Step-2: Prime Factorization of 30510

Prime factors of 30510 are 2, 3, 5, 113. Prime factorization of 30510 in exponential form is:

30510 = 2¹ × 3³ × 5¹ × 113¹

Step-3: Factors of 30504

List of positive integer factors of 30504 that divides 30504 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 41, 62, 82, 93, 123, 124, 164, 186, 246, 248, 328, 372, 492, 744, 984, 1271, 2542, 3813, 5084, 7626, 10168, 15252

Step-4: Factors of 30510

List of positive integer factors of 30510 that divides 30504 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 113, 135, 226, 270, 339, 565, 678, 1017, 1130, 1695, 2034, 3051, 3390, 5085, 6102, 10170, 15255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30504 and 30510. The biggest common factor number is the GCF number.
So the greatest common factor 30504 and 30510 is 6.

Also check out the Least Common Multiple of 30504 and 30510