Question

The least number to be multiplied with 686 to make it a perfect cube is 4. True or false​

Answer 1

Answer :-

• The given statement is true.

To find :-

Whether the statement given below is true or false :-

• The least number to be multiplied with 686 to make it a perfect cube is 4.

Step-by-step explanation :-

• To find whether the given statement is true or false, we have to find the least number which should be multiplied with 686 to make it a perfect cube.

First let's find the prime factors of 686 by prime factorisation method!

$\begin{array}{c|c} \underline2 & \underline{686} \\ \underline7 & \underline{343} \\ \underline7 & \underline{49} \\ \underline7 & \underline7 \\ & 1 \end{array}$

The given number is 686.

It can be expressed as :-

$\implies\sf 2 \times \underbrace{ 7 \times 7 \times 7}$

Since :-

• 2 is left unpaired, therefore, to make 686 a perfect cube, it should be multiplied by 2 × 2, that is, 4 [As we have to make triplets of prime factors]

Hence :-

• The least number by which 686 should be multiplied to make it a perfect cube is 4.

Thus :-

• The given statement is true.