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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.
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