Question

How do you write factors of $210$?

Answer 1

In this question, we need to find the prime factors of $210$. Here, we will determine the factors of $210$, then we will determine the prime factors of $210$, using the method of prime factorization.

Complete step-by step solution:
Here, we need to find the prime factors of $210$ using prime factorization.
We know that $210$ is a composite number.
Therefore, the possible factors of $210$ are: $210 \times 1$, $105 \times 2$, $21 \times 10$, $70 \times 3$, $30 \times 7$, $42 \times 5$,$35 \times 6$, $15 \times 14$.
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 $210$ is,
$210 = 2 \times 3 \times 7 \times 5$
This can be also written in exponential form.
So, all factors of $210$ are: $1$, $2$, $3$, $5$, $6$, $7$, $10$, $14$, $15$, $21$, $30$, $35$, $42$, $70$, $105$, $210$.

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.