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# The smallest prime number that is a factor of (1*2*3*...*30)+1 must be...

-1
456
3
+410

The smallest prime number that is a factor of (1*2*3*...*30)+1 must be...

A. less than 10
B. between 10 & 20

C. between 20 & 30

D. greater than 30

Feb 6, 2019

#1
+410
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Nvm...

Look:

1*2*3*...*30 = 30! Right?

Without even calculating you can find the answer...

Any number 30 and below will still be able to divide evenly to 30! because their number is being multiplied with 30!

But when you add the extra one,

You will always have a remainder of 1 when dividing with numbers 30 and below.

So that means numbers above 30 can be divisible to 30!

Don't you love that when you answer a though question you feel so smart. But you feel so dumb having to put it onto the forum. lol

Feb 7, 2019
#2
+110154
0

You are making me reallly think here - that is a good thing.   I have a new insight.

Your logic sounds good  but I also think that your red statment is written incorrectly......

Do you mean.

So that means NO numbers below 31 can factors of   30!+1

Melody  Feb 7, 2019
edited by Melody  Feb 7, 2019
#3
+410
0

A. less than 10
B. between 10 & 20

C. between 20 & 30

D. greater than 30

So I got the numbers above 30 right but I forgot to add 1 to 30!.

I'll rewrite the red...

So that means numbers above 30 can be divisible to 30!+1.

Feb 8, 2019