The square numbers that divide exactly into 180 are as follows :-
1² (x 180) = 180
2² (x 45) = 180
3² (x 20) = 180
6² (x 5) = 180. . . . . so 36 being 6² is the largest square number.
However, this result can be obtained from the prime factors of 180 which are :-
2² x 5 x 3² . . . . . . the squared numbers are 2 & 3. So 2x3 = 6 is the largest number that when squared, becoming equal to 36, divides exactly into 180.
32,768
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
Think of the largest number you can. Then square it. Then square that one. Since numbers don't stop, squares don't stop either.
The smallest integer is 11 but there is no smallest number! 0.11 is a smaller number and will give a perfect square. 0.0011 is smaller still, and 0.000011 even smaller. That sequence is endless!
121As 100 = 102 then the next largest square number will have to be 112 which is equal to 121.
32,768
4
25
9
81 is the largest square of a whole number...
Yes, there is. Just as there is no largest number, there is no largest square number. For example, if you calculate the square of 975, you get a number that is (a) larger than 975, and (b) by definition, a square number.
456788
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
The square of a prime number.
A number has exactly three factors if and only if it is the square of a prime number.
Think of the largest number you can. Then square it. Then square that one. Since numbers don't stop, squares don't stop either.
72/36 = 2