Question

What is the smalle
st number by which 41503 to be divided to make it a perfect square?​

Answer 1

Required Solution :

Here, we will find the smallest number by which 41503 to be divided to make it a perfect square by using prime factorization method.

$\odot$ Let us first resolve the given number into prime factors by prime factorization.

$\begin{array}{c|c} 7& \underline{41503} \\ 7&\underline{ \: 5929 \: } \\7&\underline{ \: \: 847 \: \: } \\11&\underline{ \: \: 121 \: \: } \\11&\underline{ \: \: \: 11 \: \: \: \: } \\ \: & \: 1 \: \\ \end{array}$

Now, we get that :

• 41503 = 7 × 7 × 7 × 11 × 11

Grouping into pairs :

⇒ 41503 = 7 × 7 × 7 × 11 × 11

⇒ 41503 = 7² × 11² × 7

7 left unpaired. That means,

• The smallest number by which 41503 to be divided to make it a perfect square is 7.