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56!= 1 x 2 x 3 x 4 x ... x 56

One number out of two in this product is even then 28 is the least power of 2 in 56!

7-multiple number in this product are: 7, 14, 21, 28, 35, 42, 49 = 7x7, 56

So there are 8 numbers is the product which have 7 in their decomposition

And as 49 has two 7 factors there are 9 occurence of 7 in 56!

The highest power of 14 that divides 56 is the lowest of 28(+) and 9, so it's 9

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โˆ™ 2012-09-25 20:09:57
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A polynomial of degree zero is a constant term

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Q: What is the highest power of 14 that divides 56factorial?
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