Richelle's square number

$116$ can be factorized into $29 \times 2^{2}$ . For a perfect square, it's factors must be able to pair up. Therefore, $29$ is the minimum number whose product with $116$ gives a perfect square.

$$ 116x = y^2 \Rightarrow 2^2 \times 29x = y^2 \Rightarrow 29x = \left(\frac{y}{2} \right)^2 $$

since : $$ 29 \ \textrm{is prime} \ \Rightarrow x= 29 $$

To find the smallest positive integer, we have to find the prime factors of 116. 116=2 2 29. 2 already comes two times. So we should multiply 116 with 29 to make it the square of 58

116= 2 x 2 x 29 . So multiplication by 29 makes the product a perfect square

Prime factorisation of 116 = 2 x 2 x 2

Here, pairing of 2 is completed.

So, by multiplying it by 29, it would become the square of

2 x 29 = 58

So, the answer is 29 .

$116=2^{2} \times 29$ . Therefore, the first perfect square that is divisible by 116 is $2^{2} \times 29^{2}$ , or $116 \times 29$ . The answer is 29.

We know that $116=4\cdot29$ , or $2^2\cdot29$ . We want every prime factor to be represented an even number of times, so we the smallest number is 29. Checking, $2\cdot2\cdot29\cdot29=3364$ , which indeed is a perfect square.

find the factor of 116 i.e 2 2 29 . So, answer will be 29 because multiply it with 116 give perfect square.