By which smallest number should 42592 be divided so that the quotient is a perfect cube?
Answers
your required answer is 'four' .
Given : Number = 42592
To find: the smallest number that divides a given number and gives quotient as a perfect cube
Solution : By looking at the number, we can say that it is divisible by 2
• Let us divide the given number by 2
42592 ÷ 2 = 21296
• Again divide 21296 by 2
21296 ÷ 2 = 10648
• Let's repeat this until we can't divide it furthermore
10648 ÷ 2 = 5324
5324 ÷ 2 = 2662
2662 ÷ 2 = 1331
• Now, 1331 is divisible by 11
1331 ÷ 11 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
• By doing this, we factorised 42592 in product of its prime number
42592 = 2×2×2×2×2×11×11
• Now we have to find the smallest number which can give quotient as perfect cube
• So, when we will divide given number by 4 we'll get 10648 which is cube of 22.
Hence smallest number which should divide 42592 so that the quotient is a perfect cube is 4