Divisibility Check Strategy
To find a number divisible by both 17 and 13, we need to find a number divisible by their least common multiple (LCM).
Since 17 and 13 are prime numbers, their LCM is their product:
$ \text{LCM}(17, 13) = 17 \times 13 = 221 $
Therefore, the required number must be divisible by 221.
Testing Divisibility
We will now check the divisibility of each option by 221:
- Option 1: $22372 \div 221 \approx 101.23$ (Not divisible)
- Option 2: $21401 \div 221 \approx 96.83$ (Not divisible)
- Option 3: $21658 \div 221 = 98$ (Divisible)
- Option 4: $20049 \div 221 \approx 90.72$ (Not divisible)
Conclusion
The number 21658 is the only option divisible by 221, meaning it is divisible by both 17 and 13.
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:
