Advertisements
Advertisements
Question
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:
14283
Advertisements
Solution
For each question, factorise the number into its prime factors.
14283 = 3 x 3 x 3 x 23 x 23
Grouping the factors into pairs:
14283 = (3 x 3) x (23 x 23) x 3
Here, the factor 3 does not occur in pairs. To be a perfect square, all the factors have to be in pairs. Hence, the smallest number by which 14283 must be divided for it to be a perfect square is 3.
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
7744
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
252
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
Write true (T) or false (F) for the following statement.
The square of a prime number is prime.
Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
The students of class VIII of a school donated Rs 2401 for PM's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Using prime factorisation, find which of the following are perfect squares.
484
Using prime factorisation, find which of the following are perfect squares.
729
Using prime factorisation, find the square roots of 11025
Using prime factorisation, find the square roots of 4761
