What is the Greatest Common Factor of 30144 and 30149?

Greatest common factor (GCF) of 30144 and 30149 is 1.

GCF(30144,30149) = 1

We will now calculate the prime factors of 30144 and 30149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30144 and 30149.

How to find the GCF of 30144 and 30149?

We will first find the prime factorization of 30144 and 30149. After we will calculate the factors of 30144 and 30149 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 30149

Prime factors of 30149 are 7, 59, 73. Prime factorization of 30149 in exponential form is:

30149 = 7¹ × 59¹ × 73¹

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 30149

List of positive integer factors of 30149 that divides 30144 without a remainder.

1, 7, 59, 73, 413, 511, 4307

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30144 and 30149. The biggest common factor number is the GCF number.
So the greatest common factor 30144 and 30149 is 1.

Also check out the Least Common Multiple of 30144 and 30149