Question

find the smallest number by which 10985 should be divided so that the quotient is a perfect square​

Answer 1

The smallest number by which 10985 should be divided to get the quotient as a perfect square is 65.

Step-by-step explanation:

In order to find the smallest no. by which 10985 must be divided, we will solve the given question in following steps:

(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.

Verification:

$\frac{10985}{65}$ = 169 = 13² ← 169 is a perfect square

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Answer 2

Answer:

the smallest number be which we can divide 10985 to get a perfect square is : 5 × 13 = 65

Step-by-step explanation:

To answer this question, we need to get the prime factors of the given number.

We get this as follows:

10985 = 5 × 13 × 13 × 13

This equals to:

10985 = 5 × 13 × 13²

From the prime factors, we see that we have a perfect square as 13²

So, the smallest number be which we can divide 10985 to get a perfect square is : 5 × 13 = 65