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.

Verify:

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

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Answer 2

The smallest number by which 10985 should be divided so that the quotient is a  perfect square is 65.

Step-by-step explanation:

The LCM of the number 10985 is:

10985 = 13 × 13 × 13 × 5

Now, we need to pair the same prime numbers. There is only one pair and another does not pair up.

Now, we need to the multiply the numbers that does not match.

⇒ 13 × 5 = 65

The number 10985 is need to be divided with 65.

10985 ÷ 65 = 169 = 13²