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What is the greatest power of 7 that divides into 1234!, with no remainder?

 Dec 2, 2021
 #1
avatar+117439 
+1

mm

experiment

1) How many times does 3 go into 10!

3*6*9      3 3 3 3  four times

 

10/3 = 3 and a bit

3 and a bit/3 = 1 and a bit

3+1=4

 

-------------------------------------------------

 

 

1234/7 = 176.2857142857142857

176.2/7 = 25.1

25.1/7 = 3 and a bit

3+25+176 = 204

 

So I think    204

 Dec 2, 2021
 #2
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floor[1234 / 7^1]  +  floor[1234 / 7^2]  +  floor[1234 / 7^3] ==204

 

1234!== 2^1229 * 3^614 * 5^305 * 7^204 * 11^122.......and so on. 

 Dec 3, 2021

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