What is the GCF of 54^5, 80^3, and 24?
To find the greatest common factor (GCF) of 54^5, 80^3, and 24, we need to factorize each number into their prime factors.
First, let's factorize 54:
Dividing 54 by 2, we get 27, which is an odd number.
Dividing 54 by 3, we get 18.
Dividing 18 by 2, we get 9.
Dividing 9 by 3, we get 3.
So, the prime factorization of 54 is 2×3×3×3 = 2×3^3.
Next, let's factorize 80:
Dividing 80 by 2, we get 40.
Dividing 40 by 2, we get 20.
Dividing 20 by 2, we get 10.
Dividing 10 by 2, we get 5.
So, the prime factorization of 80 is 2^4×5.
Finally, let's factorize 24:
Dividing 24 by 2, we get 12.
Dividing 12 by 2, we get 6.
Dividing 6 by 2, we get 3.
So, the prime factorization of 24 is 2^3×3.
Now, let's find the GCF by multiplying the common prime factors with the lowest exponent:
The common factors are 2 (exponent of 3), and 3.
Therefore, the GCF of 54^5, 80^3, and 24 is 2^3×3 = 8×3 = <<2^3*3=24>>24.