Question

What is the prime factorization of $800$ ?

Answer 1

Hint: In this question, we need to find express $800$ as the product of its prime factors. Here, we will determine the factors of $800$ and then we will determine the prime factors of $7429$, using the method of prime factorization.

Complete step-by-step solution:
Here, we need to find the prime factors of $800$ using prime factorization.
We know that $800$ is a composite number.
Therefore, the possible pairs of factors of $800$ are: $1 \times 800$, $2 \times 400$, $4 \times 200$, $5 \times 160$, $8 \times 100$, $10 \times 80$, $16 \times 50$, $20 \times 40$, and $32 \times 25$.
Prime factorization is a method of finding prime numbers which multiply to make the original number.
A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers.
In prime factorization, we start dividing the number by the first prime number $2$ and continue to divide by $2$ until we get a decimal or remainder. Then divide by $3,5,7,....$etc. until we get the remainder $1$ with the factors as prime numbers. Then write the numbers as a product of prime numbers.
Thus, prime factorization of $7429$ is,
$800 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5$
This can be also written in exponential form.
Hence, the $800$ can be expressed as a product of its prime factors as ${2^5} \times {5^2}$.

Note: In this question it is important to note here that a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $1$ and itself. However, the prime factorization is also known as prime decomposition. And, the prime factorization of the prime number is the number itself and $1$. Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers.