The largest three-digit number that gives the same remainder 2 when divided by 3, 5 and 9 is ________.
992
Calculation:
To find the largest three-digit number which when divided by 3, 5, and 9 leaves the same remainder 2,
we first need to find the Least Common Multiple (LCM) of these three divisors.
LCM(3, 5, 9) = 45
Now, we need to find the largest three-digit multiple of 45 and then add the remainder (2) to it.
The largest three-digit multiple of 45 is 990 (since 45 × 22 = 990).
Now, add the remainder 2 to this multiple:
990 + 2 = 992
So, the largest three-digit number that leaves a remainder of 2 when divided by 3, 5, and 9 is 992.
∴ The correct answer is 992.
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?
