What is the Greatest Common Factor of 30024 and 30030?

Greatest common factor (GCF) of 30024 and 30030 is 6.

GCF(30024,30030) = 6

We will now calculate the prime factors of 30024 and 30030, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30024 and 30030.

How to find the GCF of 30024 and 30030?

We will first find the prime factorization of 30024 and 30030. After we will calculate the factors of 30024 and 30030 and find the biggest common factor number .

Step-1: Prime Factorization of 30024

Prime factors of 30024 are 2, 3, 139. Prime factorization of 30024 in exponential form is:

30024 = 2³ × 3³ × 139¹

Step-2: Prime Factorization of 30030

Prime factors of 30030 are 2, 3, 5, 7, 11, 13. Prime factorization of 30030 in exponential form is:

30030 = 2¹ × 3¹ × 5¹ × 7¹ × 11¹ × 13¹

Step-3: Factors of 30024

List of positive integer factors of 30024 that divides 30024 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 139, 216, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 3753, 5004, 7506, 10008, 15012

Step-4: Factors of 30030

List of positive integer factors of 30030 that divides 30024 without a remainder.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 21, 22, 26, 30, 33, 35, 39, 42, 55, 65, 66, 70, 77, 78, 91, 105, 110, 130, 143, 154, 165, 182, 195, 210, 231, 273, 286, 330, 385, 390, 429, 455, 462, 546, 715, 770, 858, 910, 1001, 1155, 1365, 1430, 2002, 2145, 2310, 2730, 3003, 4290, 5005, 6006, 10010, 15015

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30024 and 30030. The biggest common factor number is the GCF number.
So the greatest common factor 30024 and 30030 is 6.

Also check out the Least Common Multiple of 30024 and 30030