What is the Greatest Common Factor of 69144 and 69150?

Greatest common factor (GCF) of 69144 and 69150 is 6.

GCF(69144,69150) = 6

We will now calculate the prime factors of 69144 and 69150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69144 and 69150.

How to find the GCF of 69144 and 69150?

We will first find the prime factorization of 69144 and 69150. After we will calculate the factors of 69144 and 69150 and find the biggest common factor number .

Step-1: Prime Factorization of 69144

Prime factors of 69144 are 2, 3, 43, 67. Prime factorization of 69144 in exponential form is:

69144 = 2³ × 3¹ × 43¹ × 67¹

Step-2: Prime Factorization of 69150

Prime factors of 69150 are 2, 3, 5, 461. Prime factorization of 69150 in exponential form is:

69150 = 2¹ × 3¹ × 5² × 461¹

Step-3: Factors of 69144

List of positive integer factors of 69144 that divides 69144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 43, 67, 86, 129, 134, 172, 201, 258, 268, 344, 402, 516, 536, 804, 1032, 1608, 2881, 5762, 8643, 11524, 17286, 23048, 34572

Step-4: Factors of 69150

List of positive integer factors of 69150 that divides 69144 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150, 461, 922, 1383, 2305, 2766, 4610, 6915, 11525, 13830, 23050, 34575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69144 and 69150. The biggest common factor number is the GCF number.
So the greatest common factor 69144 and 69150 is 6.

Also check out the Least Common Multiple of 69144 and 69150