# FIND THE LEAST NUMBER SHOULD BE DIVIDED TO GET A PERFECT SQUARE

## About "Find the least number should be divided to get a perfect square"

Find the least number should be divided to get a perfect square :

Here we are going to see how to find the least number should be divided to get a perfect square.

For this, we use the method called prime factorization.

Step 1 :

Find the prime factors of the given number.

Step 2 :

To find the square root, we have to group the factors as pairs.

Step 3 :

By grouping the factors as pairs, we may find some of the  numbers which are being extra.These are the required numbers to be divided in order make the given number as a perfect square.

Example 1 :

Find the least number by which 384 must be divided to make it a perfect square.

Solution :

Step 1 :

Let us find the prime factors of 384 using the method prime factorization.

Step 2 :

384  =  2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3

Step 3 :

‘3’ and '2' remains without a pair.

Hence, 384 must be divided by 6 to make it a perfect square.

Example 2 :

Find the smallest whole number by which the following number should be divided so as to get a perfect square.Also find the square root of the number so obtained.

2925

Solution :

Step 1 :

Let us find the prime factors of 2925 using the method prime factorization.

Step 2 :

2925  =  5 ⋅ 5 ⋅ 3 ⋅ 3 ⋅ 13

Step 3 :

‘13’ remains without a pair.

Hence, 2925 must be divide by 13 to make it a perfect square.

√(2925 ÷ 13)  =  √(5 ⋅ 5 ⋅ 3 ⋅ 3)

√225  =  5 ⋅ 3  =  15

Example 3 :

Find the smallest whole number by which the following number should be divided so as to get a perfect square.Also find the square root of the number so obtained.

1620

Solution :

Step 1 :

Let us find the prime factors of 1620 using the method prime factorization.

Step 2 :

1620  =  2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5

Step 3 :

‘5’ remains without a pair.

Hence, 1620 must be divide by 5 to make it a perfect square.

√(1620 ÷ 5)  =  √(2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3

√324  =  2 ⋅ 3 ⋅ 3  =  18

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