Question

Write the numbers \[900\] as the product of two equal factors.

Answer 1

Hint:At first, we have to find the factors of \[900\]. From them we will find the two equal factors for which the product is \[900\].
A factor is a number that divides into another number exactly and without leaving a remainder.

Complete step-by-step answer:
It is given that: The number is \[900\].
The factors of \[900\] are: \[
  1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}9,{\text{ }}10,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}20,{\text{ }}25,{\text{ }}30,{\text{ }}36,{\text{ }}45,{\text{ }}50,{\text{ }}60,\;75,{\text{ }}90,{\text{ }}100,{\text{ }}150,{\text{ }}180,{\text{ }}225,\,{\text{ }} \\
  300,{\text{ }}450,\;900. \\
 \]
\[900\] has twenty-seven factors. Among them we have to find the two equal factor for which the product is \[900\].
Let us take \[x\] to be the equal factor of \[900\] such that it gives the product as \[900\].
According to the problem,
\[x \times x = 900\]
Simplifying we get,
\[{x^2} = 900\]
Taking square root of both the sides we get,
\[x = \sqrt {900} = 30\]
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number cannot be a factor of a positive number.
Hence, the equal factor is \[30.\]

Note:Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.
The factors divide a number completely without leaving any remainder.
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number can not be a factor of a positive number.
If we divide a positive number and a negative number the quotient will be a negative number. So, we cannot take \[ - 30\] as the factor.