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In how many ways can 36 be written as the product a*b*c*d*e, where a, b, c, d, and e are positive integers such that a <= b <= c <= d <= e?

 Sep 22, 2021
 #1
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It looks like it can be written in 6 different ways:

 

11149 , 11166 , 11229 , 11236 , 11334 , 12233 , Total =  6 different ways.

 Sep 22, 2021
 #2
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how about 1 1 1 1 1 36

there is no mention that these integer have to be single digit.

Melody  Sep 22, 2021
 #3
avatar+114832 
+1

Factors of 36 are 1,2,3,4,6,9,12,18,36

 

If there are five ones then other must be 36

If there are four ones then we can have    2,18    3,12    4,9     6,6

If there are 3 ones then  2,2,9    2,3,6     3,3,4     

If there are 2 ones then   2,2,3,3  

If there is only one 1 then there are no possibilities.

 

 

So I get  1+ 4 + 3+1 = 9

 

But i have not checked it.

 Sep 22, 2021

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