If m is a digit between 0 and 9, what is the remainder when the 7

The first thing I tried to figure out here was how many of the digits really mattered. If I want to divide by 2, for instance, I only care about the units digit, since 10, 100, etc. are all multiples of 2, so they'll leave no remainder. Same idea for 4: if I want to divide by 4, I know it will go into everything from 100 on up, so I just care about the tens and units. If the last 2 digits make a multiple of 4, the whole thing is a multiple of 4.

Extending this pattern, I can notice that 16 = 2^4. This means that for a number to be a multiple of 16, it needs four 2's in its factorization. Each time I go up by a power of 10, I get another 2. So 10 is divisible by 2, 100 is divisible by 4, 1,000 is divisible by 8, and 10,000 is divisible by 16. In other words, the first three digits (1,8,m) don't matter, since that part will already be a multiple of 16. If you can recognize all this within the first 45 seconds, then you have plenty of time to deal with the rest.

From this point, I just have to divide 7359 by 16. Long division is probably the simplest way, but if you recognize that 7200 is a multiple of 16 (9*8*100), then all that's left is 159. That's one less than 160. Since it's one below a multiple of 16, it's 15 above the previous multiple.

­Hey, there is a Divisibility rule for 2 which states that :

If a no. is divisible by 2 then last digit for that no. should be divisible by 2 . For eg : 1222 ---> Last digit is 2 ,
Hence, 1222 is divisible by 2.

If a no. is divisible by 4 then last 2 digits for that no. should be divisible by 4 . For eg : 1220 ---> Last 2 digits are 20 .
Since, 20 is Divisible by 4 Hence, 1220 is divisible by 4.

If a no. is divisible by 8 then last 3 digits for that no. should be divisible by 8 . For eg : 1800 ---> Last 3 digits are 800 .
800 is Divisible by 8. Hence, 1800 is divisible by 8.

If a no. is divisible by 16 then last 4 digits for that no. should be divisible by 16. For eg : 11600 ---> Last 4 digits are 1600 .
1600 is Divisible by 16. Hence, 11600 is divisible by 16.

So, in this question, value of m doesn't matters because we can directly get the remainder by dividing 7359 by 16.

Hence, D is the answer.

Hope it helps .­

What is the remainder when the 7 digit integer 1,8m7,359 is divided by 16

Remainder of a number by 16 = Remainder of last 4 digits of the number by 16
=> Remainder of 1,8m7,359 by 16= Remainder of 7359 by 16 = 15

So, Answer will be D
Hope it helps!

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