We want to find the greatest perfect square that is a factor of the given number.
756Because this number has many factors, we will use a factor tree to write the prime factorization. We will look at the prime factors to see which ones, if any, show up twice. Then we will be able to write any perfect square factors. Let's do it!
The prime factorization shows that 756 has multiple factors that repeat themselves. Because multiple numbers show up twice, we need to think about not only the factors alone but also as pairs.
&2* 2= 4
&3* 3= 9
&(2* 3)*(2* 3)=6* 6= 36
The greatest perfect square that is a factor of 756 is 36.
Extra
Perfect Squares and Factors
Let's review the definitions of perfect square and factor.
Perfect Square
A perfect square is a number that can be written as the square of a whole number. Here are some examples.
Perfect Square
Reason
1
1^2= 1
4
2^2= 4
9
3^2= 9
16
4^2= 16
25
5^2= 25
36
6^2= 36
49
7^2= 49
64
8^2= 64
81
9^2= 81
100
10^2= 100
Factor
A factor of a number n is another number a that divides n evenly. This means that there is no remainder when you find the quotient. In other words, a is a factor of n if there exists a whole number b such that n can be written as the product of a and b.
ais a factor ofn
⇕
n÷ a = b and n=a* b
where bis a whole number
