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Find the last nonzero digit of 35!. Options
Reiko07
Posted: Wednesday, May 27, 2020 11:36:29 PM

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(1) What is the last nonzero digit of 35!?

(2) Find the last nonzero digit of 35!.

[A math quiz for Japanese high school students. (translation mine)]

I assume #1 is natural. Is #2 natural?

tautophile
Posted: Thursday, May 28, 2020 12:03:02 AM
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Yes, #2 is also natural. I'm not sure I understand the question, though. On the face of it, the last nonzero (or non-zero) digit of 35 is the 5 at the end of it. There aren't any zeros (which is what I assume is meant by "zero digit") in 35. There's a three and a five and that's all.

Could it be that the question really is "What is the last digit of 35?" without the word or concept "nonzero"?
Reiko07
Posted: Thursday, May 28, 2020 12:07:41 AM

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tautophile wrote:
Yes, #2 is also natural. I'm not sure I understand the question, though. On the face of it, the last nonzero (or non-zero) digit of 35 is the 5 at the end of it. There aren't any zeros (which is what I assume is meant by "zero digit") in 35. There's a three and a five and that's all.

Thanks, tautophile.

35! = 35 factorial = 1×2×3×···×33×34×35

The answer is 2.

35! = 10333147966386144929666651337523200000000

georgew
Posted: Thursday, May 28, 2020 1:02:28 AM

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Reiko07 wrote:
tautophile wrote:
Yes, #2 is also natural. I'm not sure I understand the question, though. On the face of it, the last nonzero (or non-zero) digit of 35 is the 5 at the end of it. There aren't any zeros (which is what I assume is meant by "zero digit") in 35. There's a three and a five and that's all.

Thanks, tautophile.

35! = 35 factorial = 1×2×3×···×33×34×35

The answer is 2.

35! = 10333147966386144929666651337523200000000

Applause Applause Applause

taurine
Posted: Thursday, May 28, 2020 4:25:18 AM

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The first sentence can be OK if you add anything else between the factor symbol and a question mark. I think that, for the avoidance of a doubt, it may be helpful to include anything else for the person who understands what mathematical factor is if the same person also knows some supplemental mathematical operators. I had seen, perhaps once, the sign > or, < included below the question mark.
Reiko07
Posted: Thursday, May 28, 2020 5:08:39 PM

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Joined: 10/30/2018
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taurine wrote:
The first sentence can be OK if you add anything else between the factor symbol and a question mark. I think that, for the avoidance of a doubt, it may be helpful to include anything else for the person who understands what mathematical factor is if the same person also knows some supplemental mathematical operators. I had seen, perhaps once, the sign > or, < included below the question mark.

Thanks, taurine. How about the following version?

(3) What is the last nonzero digit of 35! (= 35 factorial)?

tautophile
Posted: Thursday, May 28, 2020 10:52:37 PM
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Oh, I see....I didn't notice the ! that made the question refer to 35! or 35-factorial. That makes all the difference in the world. The question is about the last nonzero digit of 35!, not of 35, and it now makes sense. I assume that the value for 35! (that is, 10,333,147,966,386,144,929,666,651,337,523,200,000,000) has been correctly calculated. I checked that goggling a table of factorials that goes well beyond 35! and yes, that's the right number. (I'm glad I didn't have to calculate it myself.)

I know that N! is meant to be read and spoken as "N factorial", but I've been tempted from time to time to say "N"--a very loud, emphatic N such as might be written non-mathematically as "N!"--instead.

Drag0nspeaker
Posted: Thursday, May 28, 2020 11:34:43 PM

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tautophile wrote:
I've been tempted from time to time to say "N"--a very loud, emphatic N such as might be written non-mathematically as "N!"--instead.

Applause Applause
Ah, but that would be pronounced "N exclam".
Reiko07
Posted: Friday, May 29, 2020 1:30:17 AM

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tautophile wrote:
I checked that goggling a table of factorials that goes well beyond 35! and yes, that's the right number. (I'm glad I didn't have to calculate it myself.)

It's a "No Calculator Allowed" quiz. I used WolframAlpha to check my answer.

WolframAlpha – 35!

Here's my calculation:

35!
=
2³²×3¹⁵×5⁸×7⁵×11³×13²×17²×19×23×29×31
=
(2²⁴×3¹⁵×7⁵×11³×13²×17²×19×23×29×31)×100000000

In modulo 10,

2²⁴×3¹⁵×7⁵×11³×13²×17²×19×23×29×31

6×7×7×1×9×9×9×3×9×1

2×3×1×7

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