[tex]60 = 2 \times 2 \times 3 \times 5[/tex]
If 60 is a factor of [tex]N^2[/tex] then 2, 3 and 5 are necessarily factors of [tex]N[/tex]. So 30 is a factor of N, so 900 is a factor of [tex]N^2[/tex]. So any factors of 900 are necessarily a factor of [tex]N^2[/tex].
Let's go through the list.
15) 900/15=60, so 15 is definitely a factor of [tex]N^2[/tex].
25) 25 divides 900, definitely a factor
36) 36 divides 900, definitely a factor
100) 100 divides 900, definitely a factor
Answer: none of the above are not factors
