QR question factors

[kov82]

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A student has 30 books and wants to arrange them in rows (minimum 3 books in each row) with an equal number of books, how many ways can he arrange his books?

I said 4 ways, 3,10 10,3 5,6 6,5 but crack math says the answer is 6? and showed the factors I put plus 2,15 15,2 1,30 30,1 they said that out of these 8, 6 were possible??? it said minimum 3 books in each row or do I have the wrong idea??? it was test 11

 

[Streetwolf]

A student has 30 books and wants to arrange them in rows (minimum 3 books in each row) with an equal number of books, how many ways can he arrange his books?

I said 4 ways, 3,10 10,3 5,6 6,5 but crack math says the answer is 6? and showed the factors I put plus 2,15 15,2 1,30 30,1 they said that out of these 8, 6 were possible??? it said minimum 3 books in each row or do I have the wrong idea??? it was test 11

You could have 2 rows of 15 books but not 15 rows of 2 books.
You could have 1 row of 30 books but not 30 rows of 1 book.

So you can use 2,15 and 1,30 but not 15,2 and not 30,1.

 

[Ryltar]

First do a factor tree: 30 = 2 * 3 * 5
So...

1 row of 30
2 rows of 15
5 rows of 6
6 rows of 5
10 rows of 3
3 rows of 10