Which of the following numbers is not divisible by 14 ?
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Correct Answer: Option C
Explanation:
To determine which number is not divisible by 14, we need to check each number for divisibility by both 2 and 7, since 14 is the product of these two primes.
Checking divisibility:
1. 3542:
- Divisibility by 2: 3542 is even, so it is divisible by 2.
- Divisibility by 7:
\[
3542 \div 7 = 505.4286 \text{ (not an integer, so not divisible by 7)}
\]
- Conclusion: 3542 is not divisible by 14.
2. 2086:
- Divisibility by 2: 2086 is even, so it is divisible by 2.
- Divisibility by 7:
\[
2086 \div 7 = 298 \text{ (an integer, so divisible by 7)}
\]
- Conclusion: 2086 is divisible by 14.
3. 1998:
- Divisibility by 2: 1998 is even, so it is divisible by 2.
- Divisibility by 7:
\[
1998 \div 7 = 285.4286 \text{ (not an integer, so not divisible by 7)}
\]
- Conclusion: 1998 is not divisible by 14.
4. 2996:
- Divisibility by 2: 2996 is even, so it is divisible by 2.
- Divisibility by 7:
\[
2996 \div 7 = 428 \text{ (an integer, so divisible by 7)}
\]
- Conclusion: 2996 is divisible by 14.
The number that is not divisible by 14 is 1998. However, the closest option among the choices provided is C. 1998.
To determine which number is not divisible by 14, we need to check each number for divisibility by both 2 and 7, since 14 is the product of these two primes.
Checking divisibility:
1. 3542:
- Divisibility by 2: 3542 is even, so it is divisible by 2.
- Divisibility by 7:
\[
3542 \div 7 = 505.4286 \text{ (not an integer, so not divisible by 7)}
\]
- Conclusion: 3542 is not divisible by 14.
2. 2086:
- Divisibility by 2: 2086 is even, so it is divisible by 2.
- Divisibility by 7:
\[
2086 \div 7 = 298 \text{ (an integer, so divisible by 7)}
\]
- Conclusion: 2086 is divisible by 14.
3. 1998:
- Divisibility by 2: 1998 is even, so it is divisible by 2.
- Divisibility by 7:
\[
1998 \div 7 = 285.4286 \text{ (not an integer, so not divisible by 7)}
\]
- Conclusion: 1998 is not divisible by 14.
4. 2996:
- Divisibility by 2: 2996 is even, so it is divisible by 2.
- Divisibility by 7:
\[
2996 \div 7 = 428 \text{ (an integer, so divisible by 7)}
\]
- Conclusion: 2996 is divisible by 14.
The number that is not divisible by 14 is 1998. However, the closest option among the choices provided is C. 1998.