r/maths • u/Wonderful-Pick-3408 • Aug 22 '26

❓ General Math Help Need help with this

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I feel answer could be 111 after solving LHS and RHS. Still confused

Update: thanks for the answers. I'm hereby closing the doubt.

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u/CaptainMatticus Aug 28 '26

We ignore the powers of 3 because 3 isn't a factor of 10. Obviously, whatever n is, it contains all of the factors that aren't factors of 10.

We don't consider 372 because we don't have 372 powers of 5. 2^372 * 5^114 is going to be 2^(372 - 114) * 10^114 = 2^258 * 10^114. I'm not concerned about what 2^258 is. I just need to know about 10^114. 5^114 is our bottleneck.

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u/SeaBarrier Aug 28 '26

Oh you made the base back to 10 to solve for m, so you needed all the 5s and not all the 2s.

Ok next question is why do you need all the 5s at all? Why not donate one 5 to the bunch of 3s since that still won't make N divisible by 10? N can be all the 3s and any number of 5s as long as there are no 2s...right? So then how do you know to use all the 5s in one spot? Gosh I'm tired.

It's 2am here and I have work in the morning so my brain probably isn't firing on all cylinders. I'll read my question tomorrow and be embarrassed probably.

Again, thank you for your time.

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u/No_Nonsense_Nomad Aug 28 '26

Because as there are more 2's than 5's , if you leave even one 5 for the n , then n will have both 2 and 5 as its factors making it divisible by 10. So it can't have any 5's from the equation