What is the Greatest Common Factor of 30144 and 30156?

Greatest common factor (GCF) of 30144 and 30156 is 12.

GCF(30144,30156) = 12

We will now calculate the prime factors of 30144 and 30156, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30144 and 30156.

How to find the GCF of 30144 and 30156?

We will first find the prime factorization of 30144 and 30156. After we will calculate the factors of 30144 and 30156 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 30156

Prime factors of 30156 are 2, 3, 7, 359. Prime factorization of 30156 in exponential form is:

30156 = 2² × 3¹ × 7¹ × 359¹

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 30156

List of positive integer factors of 30156 that divides 30144 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 359, 718, 1077, 1436, 2154, 2513, 4308, 5026, 7539, 10052, 15078

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30144 and 30156. The biggest common factor number is the GCF number.
So the greatest common factor 30144 and 30156 is 12.

Also check out the Least Common Multiple of 30144 and 30156