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A factor is a number that divides into another number exactly and without leaving a remainder.

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 \[30.\]

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.