SOLUTION: Could you please help me understand how I would check for divisibility by 45. I thought you would first check for divisibility of 5 in the number and then I thought if you adde

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Could you please help me understand how I would check for divisibility by 45. I thought you would first check for divisibility of 5 in the number and then I thought if you adde      Log On


   

Question 206084: Could you please help me understand how I would check for divisibility by 45.
I thought you would first check for divisibility of 5 in the number and then I thought if you added the numbers together and they combined to give you a total of 9 then the number would be divisible by 45 but this worked for a lot of numbers I tried but then I tried 31120110 and it is not divisible by 45 so that puts my theory out.
Could you explain how I would check for divisibility of 45.
Many thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To check if a number is divisible by 45, you are correct: you check to see if it is divisible by both 5 and 9. Since the last digit of 31120110 is a 0, this means that it is divisible by 5. Because the digits add up to 9 (3+1+1+2+0+1+1+0=9), this means that the number is also divisible by 9. So this means that 31120110 is indeed divisible by 45.

Note: as a check, 31120110%2F9=691558 which confirms our answer.


Note: this theory works for any composite number. For instance, the divisibility rule for 6 states that any number is divisible by 6 if it is both divisible by 2 and 3 (which multiply to 6).