Math destroyer Test 10 #32

[SaSSyBruin]

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The question says:

For how many positive integers n is 190/n an integer?

My answer comes out to 9 but there's is 7...

It Doesn't include 1 and 190 and as positive integers that can be n.. Why not??

 

[Streetwolf]

The question says:

For how many positive integers n is 190/n an integer?

My answer comes out to 9 but there's is 7...

It Doesn't include 1 and 190 and as positive integers that can be n.. Why not??

1, 2, 5, 10, 19, 38, 95, 190

What am I missing? haha

 

[SaSSyBruin]

I meant 8 actually, maybe its a mistake.. no idea oh well

 

[azar87]

it might be a mistake did you read the solution and explanation?

 

[SaSSyBruin]

Ya they use prime factorization for some reason and they count the factors in an orderly fashion..

One factor at a time (3) : 2, 5, and 19
Two factors at a time (3): 2 X 5, 2 X 19, and 5 X 19
Three factors at a time (1): 2 X 5 X 19

still dont understand it...

 

[Streetwolf]

Ya they use prime factorization for some reason and they count the factors in an orderly fashion..

One factor at a time (3) : 2, 5, and 19
Two factors at a time (3): 2 X 5, 2 X 19, and 5 X 19
Three factors at a time (1): 2 X 5 X 19

still dont understand it...

It basically gives all the possible factors (not just primes). They just forgot to include '1' in the count.

 

[SaSSyBruin]

thanks.. ya just a mistake..

 

[NewBee12]

The answer in the Destroyer is actually 8 not 7

 

[SaSSyBruin]

maybe an old mistake oh well thanks..

 

[Maygyver]

I'm still not understanding how/why they used prime factorization.

 

[SaSSyBruin]

You don't really need to use prime factorization, they do to explain the problem for someone to solve it out.