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
-
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.
-
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 ($15 \times 66$).
-
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.
Similar Questions
- The smallest positive number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is:
- Which of the following is the least number that should be added to 3496, so that the sum is exactly divisible by 2, 6, 4 and 3
- What is the remainder when $7^{29} + 4$ is divided by 6?
- How many numbers are there between 1000 and 3000 that are completely divisible by 7?
- What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63?
- Find the remainder when $7^6 + 5$ is divided by 6.
- On dividing 15,971 by a certain number, the quotient is 55 and the remainder is 21. Find the divisor.
- A maximum of how many pieces of exact 17 cm length can be cut from a 960 cm long rod?
- A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7?
The remainder in the expression $27\frac{3}{4}$ is:
Important Questions from Divisibility and Remainder
If a five digit number 247xy is divisible by 3, 7 and 11, then what is the value of (2y - 8x)?
If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x + 3y) for x ≠ y ?
Find the greatest value of b so that 30a68b (a > b) is divisible by 11.
What is the remainder when the product of 335, 608 and 853 is divided by 13?
- What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
