What is the Greatest Common Factor of 30432 and 30450?

Greatest common factor (GCF) of 30432 and 30450 is 6.

GCF(30432,30450) = 6

We will now calculate the prime factors of 30432 and 30450, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30432 and 30450.

How to find the GCF of 30432 and 30450?

We will first find the prime factorization of 30432 and 30450. After we will calculate the factors of 30432 and 30450 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30450

Prime factors of 30450 are 2, 3, 5, 7, 29. Prime factorization of 30450 in exponential form is:

30450 = 2¹ × 3¹ × 5² × 7¹ × 29¹

Step-3: Factors of 30432

List of positive integer factors of 30432 that divides 30432 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

Step-4: Factors of 30450

List of positive integer factors of 30450 that divides 30432 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 29, 30, 35, 42, 50, 58, 70, 75, 87, 105, 145, 150, 174, 175, 203, 210, 290, 350, 406, 435, 525, 609, 725, 870, 1015, 1050, 1218, 1450, 2030, 2175, 3045, 4350, 5075, 6090, 10150, 15225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30432 and 30450. The biggest common factor number is the GCF number.
So the greatest common factor 30432 and 30450 is 6.

Also check out the Least Common Multiple of 30432 and 30450