Question

what is the smallest number by which 1372 must be multiplied so that the product is a perfect cube

Answer 1

Hello mate!!


Now if we divide, 1372 by 4, we will get7^3=343 as the quotient. So the least number you have to divide 1372 by is 4to get a perfect cube.


Hope it helps you

Answer 2

Step 1 : We will find the prime factors of 1372 by prime factorisation method

1372 = 2 × 2 × 7 × 7 × 7


Step 2 : Find the least number

If we see, the prime factors of 1372, 7 is in the group of 3 i.e. it makes a cube but 2 is not in a group of 3 i.e. it is not making a cube.


∴ $\green{\boxed{\green{\boxed{\red{\textsf{2}}}}}}$ is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube.


Let's check :

1372 × The least number

➾ 1372 × 2

➾ 2744


$^3\sqrt{2744}$ = 14


Hence, proved.