Prove that 23 is a prime number. - AQA - A-Level Maths: Mechanics - Question 5 - 2018 - Paper 2
Question 5
Prove that 23 is a prime number.
Worked Solution & Example Answer:Prove that 23 is a prime number. - AQA - A-Level Maths: Mechanics - Question 5 - 2018 - Paper 2
Step 1
Check for prime factors less than \\sqrt{23}
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Answer
To prove that 23 is a prime number, we need to check for factors up to \sqrt{23} \approx 4.8. This means we need to check the prime numbers less than or equal to 4, which are 2 and 3.
Step 2
Check divisibility by 2
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Answer
Since 23 is an odd number, it is not divisible by 2.
Step 3
Check divisibility by 3
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Answer
Next, we check if 23 is divisible by 3. Dividing 23 by 3 gives approximately 7.66, which is not an integer, indicating that 23 is not divisible by 3.
Step 4
Conclusion
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Answer
Since 23 is not divisible by any prime number less than or equal to \sqrt{23}, we conclude that 23 is a prime number.
