Introduction:
To make a number a perfect square, we need to multiply or divide it by a certain number such that the result is a perfect square. In this case, we need to find the least number by which 700 and 2817 must be multiplied or divided to make them perfect squares.

Method:
To find the least number, we will factorize the given numbers and determine the missing factors that will make them perfect squares. Then, we will calculate the square root of the missing factors to determine the least number.

Factorization of 700:
To factorize 700, we can start by finding its prime factors:
700 = 2 * 2 * 5 * 5 * 7
Lining up the factors in pairs, we have:
700 = (2 * 2) * (5 * 5) * 7

Missing factor:
To make 700 a perfect square, we need to determine the missing factor. We can see that the number 7 is not paired with any other factor. Therefore, the missing factor is 7.

Square root of the missing factor:
The square root of 7 is approximately 2.646.

Factorization of 2817:
To factorize 2817, we can start by finding its prime factors:
2817 = 3 * 3 * 313
Lining up the factors in pairs, we have:
2817 = (3 * 3) * 313

Missing factor:
To make 2817 a perfect square, we need to determine the missing factor. We can see that the number 313 is not paired with any other factor. Therefore, the missing factor is 313.

Square root of the missing factor:
The square root of 313 is approximately 17.678.

Least number:
To find the least number, we need to consider the square roots of the missing factors for both numbers, 7 and 313. The least number is the least common multiple (LCM) of these square roots.

LCM of the square roots:
The LCM of 2.646 and 17.678 is approximately 17.678.

Conclusion:
To make 700 and 2817 perfect squares, they must be multiplied or divided by approximately 17.678.