A number leaves a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7. What is the smallest positive integer that satisfies both conditions?
17
Numbers that leave remainder 2 when divided by 5: 2, 7, 12, 17, 22, 27, ...
Check each for remainder 3 when divided by 7: \(17 \div 7 = 2\) remainder \(3\), which satisfies the condition.
Verification: \(17 \div 5 = 3\) remainder \(2\), and \(17 \div 7 = 2\) remainder \(3\).
Hence, the smallest positive integer satisfying both conditions is 17.
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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:
