What is the Greatest Common Factor of 30144 and 30150?

Greatest common factor (GCF) of 30144 and 30150 is 6.

GCF(30144,30150) = 6

We will now calculate the prime factors of 30144 and 30150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30144 and 30150.

How to find the GCF of 30144 and 30150?

We will first find the prime factorization of 30144 and 30150. After we will calculate the factors of 30144 and 30150 and find the biggest common factor number .

Step-1: Prime Factorization of 30144

Prime factors of 30144 are 2, 3, 157. Prime factorization of 30144 in exponential form is:

30144 = 2⁶ × 3¹ × 157¹

Step-2: Prime Factorization of 30150

Prime factors of 30150 are 2, 3, 5, 67. Prime factorization of 30150 in exponential form is:

30150 = 2¹ × 3² × 5² × 67¹

Step-3: Factors of 30144

List of positive integer factors of 30144 that divides 30144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 157, 192, 314, 471, 628, 942, 1256, 1884, 2512, 3768, 5024, 7536, 10048, 15072

Step-4: Factors of 30150

List of positive integer factors of 30150 that divides 30144 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 67, 75, 90, 134, 150, 201, 225, 335, 402, 450, 603, 670, 1005, 1206, 1675, 2010, 3015, 3350, 5025, 6030, 10050, 15075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30144 and 30150. The biggest common factor number is the GCF number.
So the greatest common factor 30144 and 30150 is 6.

Also check out the Least Common Multiple of 30144 and 30150