What is the GCF of 54x5, 80x3, and 24?
To find the greatest common factor (GCF) of the three terms, we need to break down each term into its prime factors and then find the common factors.
The prime factorization of 54x^5 is 2 * 3^3 * x^5
The prime factorization of 80x^3 is 2^4 * 5 * x^3
The prime factorization of 24 is 2^3 * 3
To find the GCF, we take the smallest exponent for each common prime factor:
2: 3 (from 54x^5 and 24)
3: 1 (from 54x^5 and 24)
x: 3 (from 54x^5 and 80x^3)
Therefore, the GCF of 54x^5, 80x^3, and 24 is 2^3 * 3 * x^3, which simplifies to 24x^3.
that is incorrect
Apologies for the incorrect response earlier. Let's find the correct GCF for the given terms.
To find the GCF of 54x^5, 80x^3, and 24, we need to break down each term into its prime factors.
The prime factorization of 54x^5 is 2 * 3^3 * x^5.
The prime factorization of 80x^3 is 2^4 * 5 * x^3.
The prime factorization of 24 is 2^3 * 3.
To find the GCF, we take the smallest exponent for each common prime factor:
2: 3 (from 54x^5 and 24)
3: 1 (from 54x^5 and 24)
x: 3 (from 54x^5 and 80x^3)
Therefore, the GCF of 54x^5, 80x^3, and 24 is 2^3 * 3^1 * x^3, which simplifies to 24x^3.
My previous response was indeed correct.
what is 24x^3.
Apologies for the confusion caused earlier. The correct GCF of 54x^5, 80x^3, and 24 is not 24x^3, but rather 6x^3.
To explain why, let's break down the terms into their prime factors again:
The prime factorization of 54x^5 is 2 * 3^3 * x^5.
The prime factorization of 80x^3 is 2^4 * 5 * x^3.
The prime factorization of 24 is 2^3 * 3.
To find the GCF, we take the smallest exponent for each common prime factor:
2: 3 (from 54x^5 and 24)
3: 1 (from 54x^5 and 24)
x: 3 (from 54x^5 and 80x^3)
Therefore, the GCF of 54x^5, 80x^3, and 24 is 2^3 * 3^1 * x^3, which simplifies to 24x^3.