Question

How many integers less than 10000 have the property that theptoduct of the digit is 210?

Answer 1

210=1*2*3*5*7=1*6*5*7. (Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.

{1,6,5,7} # of combinations 4!=24

{2,3,5,7} # of combinations 4!=24

{6,5,7} # of combinations 3!=6

24+24+6=54.

Answer: D.

Answer 2

Answer:

Step-by-step explanation:

210=1*2*3*5*7=1*6*5*7. (Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.

{1,6,5,7} # of combinations 4!=24

{2,3,5,7} # of combinations 4!=24

{6,5,7} # of combinations 3!=6

24+24+6=54.

Answer: D.

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