Comments on: What is the largest power of 5 that divides the product of the first 100 positive integers? http://www.renewable-energy-at-home.com/uncategorized/what-is-the-largest-power-of-5-that-divides-the-product-of-the-first-100-positive-integers How you can save with renewable energy at home Thu, 10 Jun 2010 07:41:20 +0000 hourly 1 http://wordpress.org/?v=3.0 By: kb http://www.renewable-energy-at-home.com/uncategorized/what-is-the-largest-power-of-5-that-divides-the-product-of-the-first-100-positive-integers/comment-page-1#comment-862 kb Tue, 30 Jun 2009 07:17:59 +0000 http://www.renewable-energy-at-home.com/power/what-is-the-largest-power-of-5-that-divides-the-product-of-the-first-100-positive-integers#comment-862 The only numbers that contribute to this power of 5 are those that are multiples of 5. There are 100/5 = 20 multiples of 5. Also, multiples of 25 = 5^2 contribute another power of 5 apiece. There are 100/25 = 4 multiples of 25. So, the largest power of 5 dividing 100! is 20 + 4 = 24.<br><b>References : </b><br> The only numbers that contribute to this power of 5 are those that are multiples of 5. There are 100/5 = 20 multiples of 5.

Also, multiples of 25 = 5^2 contribute another power of 5 apiece.
There are 100/25 = 4 multiples of 25.

So, the largest power of 5 dividing 100! is 20 + 4 = 24.
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]]> By: Jacob http://www.renewable-energy-at-home.com/uncategorized/what-is-the-largest-power-of-5-that-divides-the-product-of-the-first-100-positive-integers/comment-page-1#comment-861 Jacob Tue, 30 Jun 2009 06:48:59 +0000 http://www.renewable-energy-at-home.com/power/what-is-the-largest-power-of-5-that-divides-the-product-of-the-first-100-positive-integers#comment-861 no solution, 5^anything cant divide anything else unless it is a multipe of 5, if u multply 2,3,4,6,7,8,9 in those 100 #s, it is impossible<br><b>References : </b><br> no solution, 5^anything cant divide anything else unless it is a multipe of 5, if u multply 2,3,4,6,7,8,9 in those 100 #s, it is impossible
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