SOLUTION: if 1st 44 positive integers form a no. N as N=12345678.........424344 and N is divided by 45, then what is the remainder?

Question 764950: if 1st 44 positive integers form a no. N as N=12345678.........424344 and N is divided by 45, then what is the remainder?
Found 2 solutions by MathLover1, 9876:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

for number to be divisible by 45 it should be divisible by both 5 and 9
as you can see, last digit is and we know that number should be divisible by both 5 and 9
for number to be divisible by last digit should be or ; so, we can say that reminder should be because only if we deduct last digit will be
so, answer is: the remainder is

but to be sure, check the divisibility by
in order to do that, we need to find the sum of the digits of N=12345678.........424344:

or, faster this way:

so sum of digits is
; so, is divisible by

since and are co-prime numbers, the number given number should also be divisible by
dividing the number by we get ;so, we got a remainder of
so, your answer is: the remainder is

Answer by 9876(1) (Show Source): You can put this solution on YOUR website!
The answer is 9 not the 4 as solved by MathLover1(7369).I guanrentee This!
The number on dividing by 5 leaves remainder 4.
Digitsum of Numbers (1234......424344)-->
The number are from 0 to 9 (Sum of digits 45)
then 10 to 19 (Digit sum 45+1x10 = 55)
then 20 to 29 (Digit sum 45+2x10 = 65)
then 30 to 39 (Digit sum 45+3x10 = 75) and
then 40 to 44 (digit sum (10+4x5 = 30)
therefore total digit sum come out to be (45+55+65+75+30 = 270)
This is divisible by 9.
When the given number is divided by 5 it leaves a remainder 4. So the number is of the form 5A + 4.
When divided by 9 it leaves a remainder 0. Hence of the form 9B+0.
Equate both the equations 5A+4=9B.
Put A= 1 and B= 1 we get 9 which is the remainder.
Try Another Example:(Very Simple1):243/45 rem is not 3 isn't it?

RELATED QUESTIONS
How many positive integers n produce a remainder of 9 when 2009 is divided by n and n > 9 (answered by drk)
If n is a positive integer then what is the remainder when {3(8n+3)+2} is divided by... (answered by josgarithmetic)
When 270 is divided by the odd number n, the quotient is a positive prime number and the (answered by solver91311)
Suppose 2001 is divided by an integer n. For which integers n is the remainder... (answered by robertb)
Suppose 2011 is divided by an integer n. For which integers n is the remainder... (answered by richard1234)
What is the smallest positive integer n so that 13n leaves a remainder of 1 when divided... (answered by Theo)
For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when... (answered by ikleyn,math_tutor2020)
if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the... (answered by ramkikk66,KMST)
When a positive integer n is divided by 6, the remainder is 2. What is the remainder when (answered by richard1234)