Question

Find the least number by which 336 be multiplied to make it a perfect square

Answer 1

Answer:

Prime factorization of 22932 gives, 22932 = 2^2 * 3^2 * 7^2 * 13 = (2*3*7)^2 * 13

Now clear and simple, dividing the number by 13 or multiplying it by 13 gives a square either way. So, 13 must be the answer for both the questions

Step-by-step explanation:

Answer 2

The least number is 21

Given : The main number is 336

To find : The least number by which 336 be multiplied to make it a perfect square.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the required least number)

First of all, we have to do prime factorisation of the main number.

So,

2| 336

_____

2| 168

_____

2| 84

____

2| 42

____

3| 21

____

7| 7

___

‎‎ㅤ1

So,

336 = 2×2×2×2×3×7

Now, we have to group the prime factors of the main number in doubles of equal factors.

So,

336 = (2×2)×(2×2)×3×7

The factors remaining outside the doubles of equal factors = 3 and 7

Now, the product of the factors remaining outside the doubles of equal factors, will be our required least number.

Our required least number = 3×7 = 21

Verification :

• (336×21) = 7056
• √7056 = (84)²
• 7056 is a perfect square

Hence, the least number is 21