What is the Greatest Common Factor of 30420 and 30432?

Greatest common factor (GCF) of 30420 and 30432 is 12.

GCF(30420,30432) = 12

We will now calculate the prime factors of 30420 and 30432, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30420 and 30432.

How to find the GCF of 30420 and 30432?

We will first find the prime factorization of 30420 and 30432. After we will calculate the factors of 30420 and 30432 and find the biggest common factor number .

Step-1: Prime Factorization of 30420

Prime factors of 30420 are 2, 3, 5, 13. Prime factorization of 30420 in exponential form is:

30420 = 2² × 3² × 5¹ × 13²

Step-2: Prime Factorization of 30432

Prime factors of 30432 are 2, 3, 317. Prime factorization of 30432 in exponential form is:

30432 = 2⁵ × 3¹ × 317¹

Step-3: Factors of 30420

List of positive integer factors of 30420 that divides 30420 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 169, 180, 195, 234, 260, 338, 390, 468, 507, 585, 676, 780, 845, 1014, 1170, 1521, 1690, 2028, 2340, 2535, 3042, 3380, 5070, 6084, 7605, 10140, 15210

Step-4: Factors of 30432

List of positive integer factors of 30432 that divides 30420 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 317, 634, 951, 1268, 1902, 2536, 3804, 5072, 7608, 10144, 15216

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30420 and 30432. The biggest common factor number is the GCF number.
So the greatest common factor 30420 and 30432 is 12.

Also check out the Least Common Multiple of 30420 and 30432