Is 115 prime?
Understand the Problem
The question is asking whether the number 115 is a prime number. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. We will check if there are any divisors of 115 other than 1 and 115 itself.
Answer
115 is not a prime number.
Answer for screen readers
The number 115 is not a prime number.
Steps to Solve
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Identify Divisors of 115 To determine if 115 is prime, we need to check if it has any divisors other than 1 and 115 itself. We can start by checking for divisibility by smaller prime numbers.
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Check Divisibility by 2 Check if 115 is divisible by 2. Since 115 is an odd number, it is not divisible by 2.
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Check Divisibility by 3 Next, we check if 115 is divisible by 3. We add the digits of 115: $1 + 1 + 5 = 7$. Since 7 is not divisible by 3, 115 is not divisible by 3.
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Check Divisibility by 5 Now, check divisibility by 5. A number is divisible by 5 if its last digit is 0 or 5. The last digit of 115 is 5, so: $$ 115 \div 5 = 23 $$ Thus, 115 is divisible by 5, indicating that it has divisors other than 1 and itself.
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Conclude About Primality Since we found that 115 has a divisor (5), we conclude that 115 is not a prime number.
The number 115 is not a prime number.
More Information
115 is an example of a composite number because it can be divided by numbers other than 1 and itself. Specifically, it can be factored into $5 \times 23$, showing that there are factors other than 1 and 115.
Tips
A common mistake is to assume that just because a number is odd or ends in 5, it is prime. It is essential to check for divisibility by relevant prime numbers to establish primality accurately.
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