Photo AI
Prove that 23 is a prime number. - AQA - A-Level Maths: Pure - 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: Pure - Question 5 - 2018 - Paper 2
Step 1
Step 1: Check for factors of 23
Answer
To determine if 23 is a prime number, we first need to check if it has any divisors other than 1 and itself. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
We only need to check for prime factors that are less than or equal to the square root of 23. The approximate value of the square root of 23 is:
Thus, we will check the prime numbers less than or equal to 4.8, which are 2 and 3.
Step 2
Step 2: Determine divisibility
Answer
Next, we will determine if 23 is divisible by 2 or 3:
- Divisibility by 2: 23 is odd, therefore it is not divisible by 2.
- Divisibility by 3: To check divisibility by 3, we calculate the sum of the digits of 23:
Since 5 is not divisible by 3, 23 is not divisible by 3 either.
Step 3