the answer is 46. I am not able to figure out how to arrive at that answer
Asked
Active
Viewed 857 times
-1
-
Hint: 10 is a bit large, try it for a smaller number. Like $3$ or $5$. For small numbers you should be able to write everything out. – lulu Aug 03 '15 at 14:40
2 Answers
1
Well, actually you can't arrive at the answer, because the answer should be 48.
The long way is to list all factors of 2520, viz. 1 through 10, 12,14,15, ... 2520
but the theory of numbers says that if you break them up into prime factors, viz $2^3 \cdot3^2 \cdot 5^1 \cdot 7^1$,
add 1 to each of the indices and multiply them out, you get the answer: $4\cdot3\cdot2\cdot2 = 48$
Look here to see all 48 factors
NOTE
The term proper factor should have been used in the question to get the answer of 46, but if you have been taught to exclude 1 & the number anyway, just subtract 2 from the number theory computation.
true blue anil
- 41,295
-
I suspect they may be looking for proper factors only (excluding $1$ and $K$), in which case subtracting $2$ from your answer gives the desired one. – Cameron Buie Aug 03 '15 at 15:40
-
-
It may be an explicit part of the text's definition of "factor" (though that seems like a bad idea to me). – Cameron Buie Aug 03 '15 at 15:47
-
-
-
-
0
The least positive integer divisible by $1,2,3,4$ is $4\cdot 3 = 12$. Note that it is not $2\cdot 3\cdot 4 = 24$ - we don't need to include the $2$, because any integer that is divisible by $4$ is also divisible by $2$.
Now you need to generalize that idea to $1,2,\cdots,10$.
fgp
- 21,050
-
Ok so I get: 9, 8, 7, 5 (using divisibility rules). And 987*5= 2520. How do I proceed after that? Thank you for the help – PEFGreAspirant Aug 03 '15 at 14:54