What is the Greatest Common Factor of 54144 and 54150?

Greatest common factor (GCF) of 54144 and 54150 is 6.

GCF(54144,54150) = 6

We will now calculate the prime factors of 54144 and 54150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54144 and 54150.

How to find the GCF of 54144 and 54150?

We will first find the prime factorization of 54144 and 54150. After we will calculate the factors of 54144 and 54150 and find the biggest common factor number .

Step-1: Prime Factorization of 54144

Prime factors of 54144 are 2, 3, 47. Prime factorization of 54144 in exponential form is:

54144 = 2⁷ × 3² × 47¹

Step-2: Prime Factorization of 54150

Prime factors of 54150 are 2, 3, 5, 19. Prime factorization of 54150 in exponential form is:

54150 = 2¹ × 3¹ × 5² × 19²

Step-3: Factors of 54144

List of positive integer factors of 54144 that divides 54144 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64, 72, 94, 96, 128, 141, 144, 188, 192, 282, 288, 376, 384, 423, 564, 576, 752, 846, 1128, 1152, 1504, 1692, 2256, 3008, 3384, 4512, 6016, 6768, 9024, 13536, 18048, 27072

Step-4: Factors of 54150

List of positive integer factors of 54150 that divides 54144 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 25, 30, 38, 50, 57, 75, 95, 114, 150, 190, 285, 361, 475, 570, 722, 950, 1083, 1425, 1805, 2166, 2850, 3610, 5415, 9025, 10830, 18050, 27075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54144 and 54150. The biggest common factor number is the GCF number.
So the greatest common factor 54144 and 54150 is 6.

Also check out the Least Common Multiple of 54144 and 54150