How many times can 30! be divided by 10?

[YAMATO2201]

Yamato2201,

Have you Japanese people never heard of the calculator?

How many times can 30! be divided by 10?

30÷5=6
6÷5=1.2
1.2÷5<1
6+1=7
30÷2=15>7
Hence, the answer is 7 times.

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How many times can 3000! be divided by 10?

3000÷5=600
600÷5=120
120÷5=24
24÷5=4.8
4.8÷5<1
600+120+24+4=748
3000÷2=1500>748

Hence, the answer is 748 times.

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No Calculator Needed!

 

[jutfrank]

This video featuring a Japanese schoolkid using an imaginary abacus (jump to 1:20) made a big impression on me when I first saw it.

https://www.youtube.com/watch?v=6m6s-ulE6LY

 

[bubbha]

How many times can 30! be divided by 10?

30÷5=6
6÷5=1.2
1.2÷5<1
6+1=7
30÷2=15>7
Hence, the answer is 7 times.

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

How many times can 3000! be divided by 10?

3000÷5=600
600÷5=120
120÷5=24
24÷5=4.8
4.8÷5<1
600+120+24+4=748
3000÷2=1500>748

Hence, the answer is 748 times.

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

No Calculator Needed!

Cool!

Basically it's tallying up the 5s. And since there are more 2s than 5s, the number of 5s is the same as the number of 10s. All you need to do is count the 5s! Nice trick!

 

[YAMATO2201]

The missing word is "evenly." How many times can it be divided evenly.

Is the following sentence natural?

Find the smallest positive integer n such that (n+1)(n+3)(n+5) can be divided evenly by 1000.

(my original quiz)

 

[GoesStation]

Is the following sentence natural?

Find the smallest positive integer n such that (n+1)(n+3)(n+5) can be divided evenly by 1000.

(my original quiz)

It looks fine to me.