SOLUTION: 20!= 20x19x18x17x...x3x2x1. If 20! is written in its prime factorization form, what is the power of 5?

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Question 943702: 20!= 20x19x18x17x...x3x2x1. If 20! is written in its prime factorization form, what is the power of 5?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Write out 20%21 fully to get

20!= 20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

Now I'm going to highlight in red the factors that are multiples of 5

20!= 20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

So we have 20, 15, 10, 5

20 = 5*4
15 = 5*3
10 = 5*2
5 = 5*1

We have four copies of '5' being multiplied here. So we have 5%5E4 as a factor of 20%21