Question 669969: Can anyone walk me through how to solve: N=1X2X3X4...X20 how many terminal zeros will N have
I found a "solution" that uses prime number factors, but I do not understand how prime numbers help solve this problem. Can some one explain this to me? Thank you so much!
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! If e means even and o means odd,
These are some multiplication rules:
e x e = e
e x o = e
o x o = o
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The first terminal zero appears when you
multiply
o x e x o x e x 5 and this is
e x e x 5
e x 5
which gives me a terminal zero. If it was
o x 5, I would have a terminal 5
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Now, continuing,
e x 0 x e x o x 10
e x e x 10
e x 10
which gives me 2 terminal zeros so far
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o x e x o x e x 15
e x e x 15
e x 15
which gives another terminal zero, 3 so far
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e x o x e x o x 20
e x e x 20
e x 20
the last terminal zero, 4 total
You can check on a calculator. Find 20!
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