What is the Greatest Common Factor of 39144 and 39150?

Greatest common factor (GCF) of 39144 and 39150 is 6.

GCF(39144,39150) = 6

We will now calculate the prime factors of 39144 and 39150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39144 and 39150.

How to find the GCF of 39144 and 39150?

We will first find the prime factorization of 39144 and 39150. After we will calculate the factors of 39144 and 39150 and find the biggest common factor number .

Step-1: Prime Factorization of 39144

Prime factors of 39144 are 2, 3, 7, 233. Prime factorization of 39144 in exponential form is:

39144 = 2³ × 3¹ × 7¹ × 233¹

Step-2: Prime Factorization of 39150

Prime factors of 39150 are 2, 3, 5, 29. Prime factorization of 39150 in exponential form is:

39150 = 2¹ × 3³ × 5² × 29¹

Step-3: Factors of 39144

List of positive integer factors of 39144 that divides 39144 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 233, 466, 699, 932, 1398, 1631, 1864, 2796, 3262, 4893, 5592, 6524, 9786, 13048, 19572

Step-4: Factors of 39150

List of positive integer factors of 39150 that divides 39144 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 29, 30, 45, 50, 54, 58, 75, 87, 90, 135, 145, 150, 174, 225, 261, 270, 290, 435, 450, 522, 675, 725, 783, 870, 1305, 1350, 1450, 1566, 2175, 2610, 3915, 4350, 6525, 7830, 13050, 19575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39144 and 39150. The biggest common factor number is the GCF number.
So the greatest common factor 39144 and 39150 is 6.

Also check out the Least Common Multiple of 39144 and 39150