For 144:
2 x 8 x 9
4 x 4 x 9
3 x 6 x 8
3 x 3 x 16
2 x 3 x 24
2 x 2 x 36
2 x 4 x 18
3 x 4 x 12
2 x 6 x 12
For 300:
2 x 6 x 25
2 x 10 x 15
2 x 3 x 50
2 x 5 x 30
3 x 4 x 25
3 x 5 x 20
3 x 10 x 10
5 x 6 x 10
2 x 2 x 75
4 x 5 x 15
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The prime factors of 144 are 2(4) and 3(2)That is, 144 = 2 x 2 (4 times) x 3 x 3, and those numbers are primes.
There are 10 of them. Only the squares of 1 and 11 cannot be made in such a way.
Since there is only one square of 12 (= 144) there is not much of a pattern.
25 and 144
Only 144 is equal to 144. No other number is equal to 144.