What is the Greatest Common Factor of 30132 and 30144?

Greatest common factor (GCF) of 30132 and 30144 is 12.

GCF(30132,30144) = 12

We will now calculate the prime factors of 30132 and 30144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30132 and 30144.

How to find the GCF of 30132 and 30144?

We will first find the prime factorization of 30132 and 30144. After we will calculate the factors of 30132 and 30144 and find the biggest common factor number .

Step-1: Prime Factorization of 30132

Prime factors of 30132 are 2, 3, 31. Prime factorization of 30132 in exponential form is:

30132 = 2² × 3⁵ × 31¹

Step-2: 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-3: Factors of 30132

List of positive integer factors of 30132 that divides 30132 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 31, 36, 54, 62, 81, 93, 108, 124, 162, 186, 243, 279, 324, 372, 486, 558, 837, 972, 1116, 1674, 2511, 3348, 5022, 7533, 10044, 15066

Step-4: Factors of 30144

List of positive integer factors of 30144 that divides 30132 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30132 and 30144. The biggest common factor number is the GCF number.
So the greatest common factor 30132 and 30144 is 12.

Also check out the Least Common Multiple of 30132 and 30144