Is 365 a prime number? Explain your answer.
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No, 365 is not a prime number.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and itself.
To check whether 365 is prime, we need to test whether it is divisible by any integer between 2 and the square root of 365 (rounded up to the nearest integer). The square root of 365 is approximately 19.1, so we need to test whether 365 is divisible by any integer between 2 and 20.
We can see that 365 is divisible by 5 and 73:
365 ÷ 5 = 73 365 ÷ 73 = 5
Since 365 is divisible by factors other than 1 and itself, it is not a prime number. It is a composite number that can be expressed as the product of two prime factors: 5 and 73.