Finding Least Number for Divisibility
The problem asks for the smallest number that, when added to 1000, results in a sum that is perfectly divisible by 15.
Divisibility Calculation
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First, find the remainder when 1000 is divided by 15.
Using division: $1000 \div 15$ $1000 = 15 \times 66 + 10$ The quotient is 66 and the remainder is 10.
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To make 1000 divisible by 15, we need to reach the next multiple of 15. The current number (1000) is 10 more than a multiple of 15 ($15 \times 66$).
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The amount needed to reach the next multiple of 15 is calculated by subtracting the remainder from the divisor (15).
Least number to add $= 15 - \text{Remainder}$ $= 15 - 10$ $= 5$
Therefore, the least number which when added to 1000 gives a number exactly divisible by 15 is 5. Adding 5 to 1000 gives 1005, and $1005 \div 15 = 67$, confirming it is exactly divisible.
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Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
