Question

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

Answer 1

Step-by-step explanation:

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}

65

10985

= 169 = 13² ← 169 is a perfect square

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Answer 2

Answer:

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}

65

10985

= 169 = 13² ← 169 is a perfect square

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