# How do you write 140 as the product of its prime factors?

Sep 10, 2016

$140 = 2 \times 2 \times 5 \times 7$

#### Explanation:

To write any number as a product of its prime factors, we should find all those prime numbers which when multiplied together form the number. Note that in such factorization, prime numbers can get repeated as well, but what is important is that

(1) all numbers are prime

(2) and their product is given number

Hence, we should divide the given number consistently by prime numbers starting with $2$, which is first prime number and continue till all factors are prime numbers.

Before we try this for given number $140$, let us list first few prime numbers, which are $\left\{2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , \ldots\right\}$

Now $140$

= $2 \times 70$ (and as $70$ can be divided by $2$ again)

= $2 \times 2 \times 35$

= $2 \times 2 \times 5 \times 7$

As now we have all prime factors, the process is complete and prime factors of $140$ are $2 \times 2 \times 5 \times 7$.