Question

.Find the least number by which 31752must be divided to get a perfect square .Also find the square root of the resulting number

(with explanation)​

Answer 1

Step-by-step explanation:

To find the least number by 31752 should be divided so that the resulting

number becomes a perfect square, we have to find the prime factorization of 31752

Prime factorization of 31752

___________

2 | 31752

|___________

2 | 15876

|___________

2 | 7938

|___________

3 | 3969

|___________

3 | 1323

|___________

3 | 441

|___________

3 | 147

l___________

7 l 49

l___________

7 l 7

l___________

7 l 1

l___________

Prime factorization of 31752 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7 x 7

We can see that only 2 and 7 are unpaired.

So, 2 x 7 = 14, is the least number should be divided so that the resulting

number is a perfect square.

Let us check it.

31752 ÷ 14 = 2268

√2268 = 47

Hence proved.

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