find the smallest number by which 10985 should be divided so that the quotient is a perfect square
Answers
Step-by-step explanation:
let that smallest no be x since the no get divide so no rimender left so we can say √10985 X x = perfect square
The smallest number by which 10985 should be divided to get the quotient as a perfect square is 65.
Step-by-step explanation:
(1). First we will find the prime factors of the number 10985.
5 | 10985
-----------
13 | 2197
------------
13 | 169
------------
13 | 13
10985 = 5 * 13 * 13 * 13
(2). Now we will find for common pairs from the prime factors so received
Pair: 13 * 13
Non-pair: 5 * 13
Here we get the 13 as a common pair and another 13 with 5 is left out.
∴ We will have to divide 10985 with 13*5 = 65.
Thus, the required smallest no. is 65 which when divides 10985 will give the quotient as a perfect square.
Check:
10985/65 = 169 = 13^2 ← 169 is a perfect square
-------------------------------------------------------------------------------------------------
Also View:
Find the smallest number by which 17496 must be divided ,so that the quotient is a perfect cube.also find the cube root of the quotient ?
https://brainly.in/question/4804318
Find the smallest number by which 3150 be divided so that the quotient is a perfect square?
https://brainly.in/question/9435205