Question

Write the prime factorization of $56$ using the division method.

Answer 1

Hint: In this question, we need to find express $56$ as the product of its prime factors. Here, we will determine the prime factors of $56$ using the method of prime factorization. In this method, we start dividing the number by its constituent prime factors till we reach the number $1$. Then, we express the original number as the product of its constituent prime factors.

Complete step by step solution:
We need to find the prime factors of $56$ using the division method.
We know that $56$ is a composite number.
So, we have,
\[\begin{align}
  & 2\left| \!{\underline {\,
  56\,}} \right. \\
 & 2\left| \!{\underline {\,
  28\,}} \right. \\
 & 2\left| \!{\underline {\,
  14\,}} \right. \\
 & 7\left| \!{\underline {\,
  7\,}} \right. \\
 \end{align}\]
Thus, prime factorization of $56$ is,
$56 = 2 \times 2 \times 2 \times 7$
Expressing in the powers of constituent prime factors, we get,
$56 = {2^3} \times 7$
This is the required answer.
Therefore, the prime factorization of $56$ is $ {2^3} \times 7$.

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.