Question

Express the following number as a product of power of prime factor.
1000

Answer 1

Hint: Here, we have to express 1000 as a product of power of prime factors. For this, we will divide 1000 by smaller prime number 2. If 1000 is divisible by 2 then the quotient obtained will again be divided by 2. If 2 does not divide 1000, we will move to next prime number 3 and so on.
Using this, we will keep on dividing 1000 by prime numbers until we get quoting as 1. All the prime numbers will then be written in the product form. After that, we will write some prime numbers as their powers and hence, obtain the required answer.

Complete step by step answer:
We are given numbers as 1000.
Let us try to divide it by 2 which is the smallest prime number. We get $\dfrac{1000}{2}=500$.
Therefore, 2 is one of the prime factors.
Now let us divide the obtained quotient (500) by 2 we get $\dfrac{500}{2}=250$. Therefore, 2 is again a prime factor.
Dividing 250 by 2, we get $\dfrac{250}{2}=125$ , so 2 is again a prime factor.
Dividing 125 by 2, we get $\dfrac{125}{2}=62.5$ which is not the whole number, so 2 does not divide 125.
Dividing 125 by 3, we get $\dfrac{125}{3}=41.6$ which is not the whole number, so 3 does not divide 125.
Divide 125 by 5, we get $\dfrac{125}{5}=25$ , so 5 is a prime factor.
Also, we know, $5\times 5=25$ , so two more 5 are prime factors.
Hence all the prime factors are $2,2,2,5,5,5$.
Now, 1000 can be written in the form as $1000=2\times 2\times 2\times 5\times 5\times 5$.
Expressing 2 and 5 in powers, we get $1000={{2}^{3}}\times {{5}^{3}}$.

Hence, 1000 can be written as ${{2}^{3}}\times {{5}^{3}}$ as product of power of prime factors.

Note: To save time, students can also use the divisibility rule of 2, 3 and 5 to check if the number is divisible by them. Divisibility rule of 2 states that one’s place should have 0, 2, 4, 6, 8. Divisibility rule of 3 states that, sum of all digits of a number should be divisible by 3. Divisibility rule of 5 states that one’s place should have 0 or 5. While forming prime factors, make sure you consider all the 2's and 5's.