What is the Greatest Common Factor of 24000 and 24015?

Greatest common factor (GCF) of 24000 and 24015 is 15.

GCF(24000,24015) = 15

We will now calculate the prime factors of 24000 and 24015, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24000 and 24015.

How to find the GCF of 24000 and 24015?

We will first find the prime factorization of 24000 and 24015. After we will calculate the factors of 24000 and 24015 and find the biggest common factor number .

Step-1: Prime Factorization of 24000

Prime factors of 24000 are 2, 3, 5. Prime factorization of 24000 in exponential form is:

24000 = 2⁶ × 3¹ × 5³

Step-2: Prime Factorization of 24015

Prime factors of 24015 are 3, 5, 1601. Prime factorization of 24015 in exponential form is:

24015 = 3¹ × 5¹ × 1601¹

Step-3: Factors of 24000

List of positive integer factors of 24000 that divides 24000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 125, 150, 160, 192, 200, 240, 250, 300, 320, 375, 400, 480, 500, 600, 750, 800, 960, 1000, 1200, 1500, 1600, 2000, 2400, 3000, 4000, 4800, 6000, 8000, 12000

Step-4: Factors of 24015

List of positive integer factors of 24015 that divides 24000 without a remainder.

1, 3, 5, 15, 1601, 4803, 8005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24000 and 24015. The biggest common factor number is the GCF number.
So the greatest common factor 24000 and 24015 is 15.

Also check out the Least Common Multiple of 24000 and 24015