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# How many trailing zeroes does 24!+25! has?

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Re: How many trailing zeroes does 24!+25! has? [#permalink]
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24! + 25!
= 24! + 25*24!
= 24!(1 + 25)
= 24! * 13 * 2

The zeroes are contributed only by the number of 5's in 24! --> 4 trailing zeroes

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How many trailing zeroes does 24!+25! has? [#permalink]
Vyshak wrote:
24! + 25!
= 24! + 25*24!
= 24!(1 + 25)
= 24! * 13 * 2

The zeroes are contributed only by the number of 5's in 24! --> 4 trailing zeroes

hi Vyshak
I understand you how got this 24!(1 + 25) by factoring out but what function does this (1 + 25) / or (13 * 2) this have , and how is it called ?
thanks

hi there pushpitkc maybe you can explain YAY

Originally posted by dave13 on 02 Aug 2018, 08:28.
Last edited by dave13 on 06 Aug 2018, 02:12, edited 2 times in total.
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How many trailing zeroes does 24!+25! has? [#permalink]
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dave13 wrote:
Vyshak wrote:
24! + 25!
= 24! + 25*24!
= 24!(1 + 25)
= 24! * 13 * 2

The zeroes are contributed only by the number of 5's in 24! --> 4 trailing zeroes

hi Vyshak
I understand you how got this 24!(1 + 25) by factoring out but what function does this (1 + 25) / or (13 * 2) this have , and how is it called ?
thanks

hi there pushpitkc maybe you can explain YAY

Hey dave13

That way you can check if another 0 can be formed making the trailing zeroes
becomes greater.

For example, if we have 24! * 25, then the trailing zeroes will be 6(not 4)

I think you know that the number of zeroes in 24! is determined by multiplying
the highest power of 5 with the 2 - 24!(which is 24*23*22*21..*3*2*1) will have
four 5's(one each from 5, 10, 15, and 20) and many more than four 2'(minimum
of 6 - one from 2 and 6, two from 4, and three from 8)

Now, the 25 which has two more 5's multiply with the 2's from 8 and thereby, the
expression ends with six 0's(instead of four)

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Re: How many trailing zeroes does 24!+25! has? [#permalink]
pushpitkc wrote:
dave13 wrote:
Vyshak wrote:
24! + 25!
= 24! + 25*24!
= 24!(1 + 25)
= 24! * 13 * 2

The zeroes are contributed only by the number of 5's in 24! --> 4 trailing zeroes

hi Vyshak
I understand you how got this 24!(1 + 25) by factoring out but what function does this (1 + 25) / or (13 * 2) this have , and how is it called ?
thanks

hi there pushpitkc maybe you can explain YAY

Hey dave13

That way you can check if another 0 can be formed making the trailing zeroes
becomes greater.

For example, if we have 24! * 25, then the trailing zeroes will be 6(not 4)

I think you know that the number of zeroes in 24! is determined by multiplying
the highest power of 5 with the 2 - 24!(which is 24*23*22*21..*3*2*1) will have
four 5's(one each from 5, 10, 15, and 20) and many more than four 2'(minimum
of 6 - one from 2 and 6, two from 4, and three from 8)

Now, the 25 which has two more 5's multiply with the 2's from 8 and thereby, the
expression ends with six 0's(instead of four)

thank you

24! * 25 = $$\frac{24}{5}$$ +$$\frac{25}{5^2}$$ = 4+2 = 6

is my understanding correct ?
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How many trailing zeroes does 24!+25! has? [#permalink]
slight mistake !!
it should be 24! (1 + 25) = 24! * 26
since 26 doesn't have a 5 in it , we are only concerned with number of 5's in 24!
which is 4
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Re: How many trailing zeroes does 24!+25! has? [#permalink]
Correct me if I am wrong but if we don't take the common term out 24! yields 4 trailing places and 25! yields 6. The two extra 0's in 25! will convert to non zero integers when 24! is added in so 4 is the answer
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Re: How many trailing zeroes does 24!+25! has? [#permalink]
Hello experts!