Question

What is an exponent of 3 in the prime factorization of 864?

Answer 1

Hint: Here in this question, we have to find the exponent of the number 3. The number 864 is factored by using the prime numbers and the obtained result is written in the form of exponent. Here we use the simple arithmetic operations and hence we determine the required solution for the given question.

Complete step-by-step answer:
An exponent refers to the number of times a number is multiplied by itself. In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
 Now we divide the number 864 by using the prime numbers.
When we divide the number 864 by 3, and the number 864 is written as
\[864 = 3 \times 288\]
When we divide the number 288 by 3, and the number 864 is written as
\[864 = 3 \times 3 \times 96\]
When we divide the number 96 by 3, and the number 864 is written as
\[864 = 3 \times 3 \times 3 \times 32\]
When we divide the number 32 by 2, and the number 864 is written as
\[864 = 3 \times 3 \times 3 \times 2 \times 16\]
When we divide the number 16 by 2, and the number 864 is written as
\[864 = 3 \times 3 \times 3 \times 2 \times 2 \times 8\]
When we divide the number 8 by 2, and the number 864 is written as
\[864 = 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 4\]
When we divide the number 4 by 2, and the number 864 is written as
\[864 = 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2\]
Therefore the number 864 in the exponent it is written as
\[864 = {3^3} \times {2^4}\]
Therefore the exponent of 3 in the prime factorization of 864 is 3.
So, the correct answer is “3”.

Note: Here while solving this problem we must and should know about the table of multiplication and writing the number into the form of exponents. We can divide the number 864 by using the prime numbers, where prime numbers are defined as the number which is divisible by 1 and the number itself.