Is 253 prime?
Understand the Problem
The question is asking whether the number 253 is a prime number, which means it can only be divided by 1 and itself without resulting in a fraction. We will check for divisibility by prime numbers up to the square root of 253.
Answer
No, 253 is not a prime number.
Answer for screen readers
The number 253 is not a prime number.
Steps to Solve
- Determine the square root of 253
The first step is to find the square root of 253 to know the range of prime numbers we need to check.
$$ \sqrt{253} \approx 15.9 $$
So we need to check for prime numbers up to 15.
- List prime numbers up to 15
The prime numbers less than or equal to 15 are 2, 3, 5, 7, 11, and 13.
- Check divisibility by 2
253 is odd, so it is not divisible by 2.
- Check divisibility by 3
Sum the digits of 253:
$$ 2 + 5 + 3 = 10 $$
Since 10 is not divisible by 3, 253 is not divisible by 3.
- Check divisibility by 5
Since 253 does not end in 0 or 5, it is not divisible by 5.
- Check divisibility by 7
Divide 253 by 7:
$$ 253 \div 7 = 36.142857... $$
Since the result is not an integer, 253 is not divisible by 7.
- Check divisibility by 11
Alternate sum of the digits of 253:
$$ 2 - 5 + 3 = 0 $$
Since 0 is divisible by 11, 253 is divisible by 11.
Therefore, since 253 is divisible by 11, it is not a prime number.
The number 253 is not a prime number.
More Information
253 is divisible by 11, specifically, 253 = 11 * 23.
Tips
A common mistake is to forget checking all prime numbers up to the square root of the given number for divisibility.