Question

Find the least number which must be divided by 10648 to make it a perfect square.

Answer 1

Answer:

It can be divided by 7 to make it a perfect square of 144

Step-by-step explanation:

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Answer 2

Given : The main number = 10648

To find : The least number by which the main number should be divided to make the main number a perfect square.

Solution :

The least number is 22

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to find the said least number)

First of all we have to do the prime factorisation of the main number.

So,

2 | 10648

________

2 | 5324

________

2 | 2662

________

11 | 1331

________

11 | 121

________

11‎ | 11

________

ㅤㅤ1

Which implies,

10648 = 2×2×2×11×11×11 (product of prime factors)

Now, we have to group the factors in the doubles of equal factors.

10648 = 2 × (2×2) × 11 × (11×11)

Our required least number will be the product of the leftover factors which our outside the doubles of equal factors.

Remaining factors = 2 and 11

So, The required least number = 2 × 11 = 22

Verification :

• 10648 ÷ 22 = 484
• 484 = (22)² (a perfect square)

Hence, the least number is 22