Question

Express 210 as the product of prime factors.

Answer 1

Hint:Divide the number using prime numbers according to divisibility. Divide until the reminder is a prime number.

Complete step-by-step answer:
The method of prime factorization is used to “break down” or express a given number as a product of prime numbers.
The prime numbers will occur more than once in the prime factorization and they can be expressed together in an exponential form to look compact.
Where prime numbers is a whole number which is greater than 1, it is only divisible by 1 and itself.
i.e. prime number has two factors namely 1 and itself
We have the number 210
$\begin{array}{rl}& 2|\underset{―}{210}\\ & 3|\underset{―}{105}\\ & 5|\underset{―}{35}\\ & 7\end{array}$
Divide 210 by prime number 2 , divide the reminder 105 by 3 until it becomes indivisible
$\therefore 210=2\times 3\times 5\times 7$
$\therefore$The prime factorization of $210=2\times 3\times 5\times 7$

Note: This can also be solved by breaking 210 into two parts 10 and 21 such that the product is 210 and again breaking 10 and 21 we get 5,2 ,3 and 7 prime factors.

$\therefore$ The prime factorization of
$\begin{array}{rl}& 210=5\times 2\times 3\times 7\\ & =2\times 3\times 5\times 7\end{array}$