Is 209 prime?
Understand the Problem
The question is asking whether the number 209 is a prime number, which means it should be divided by any integers other than 1 and itself without leaving a remainder.
Answer
No
Answer for screen readers
No, 209 is not a prime number because it is divisible by 11.
Steps to Solve
- Check divisibility by small prime numbers (2, 3, 5, etc.)
Start by checking if 209 is divisible by common small primes. We do this because if a number is not divisible by any small primes, it is likely prime.
- Check divisibility by 2
Since 209 is odd, it is not divisible by 2.
- Check divisibility by 3
Add the digits of 209: $2 + 0 + 9 = 11$. Since 11 is not divisible by 3, 209 is not divisible by 3.
- Check divisibility by 5
Since 209 does not end in 0 or 5, it is not divisible by 5.
- Check divisibility by 7
Divide 209 by 7: $209 \div 7 = 29.8571$. Since this is not an integer, 209 is not divisible by 7.
- Check divisibility by 11
Alternate sum of the digits is $2 - 0 + 9 = 11$. Since 11 is divisible by 11, 209 is divisible by 11.
Since 209 is divisible by 11, it is not a prime number.
No, 209 is not a prime number because it is divisible by 11.
More Information
The number 209 is divisible by 11, thus it is not a prime number.
Tips
A common mistake is to not check divisibility by all small prime numbers. For conclusive results, ensure that you check divisibility by at least the prime numbers less than the square root of the number in question.
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