The first- floor apartments in Jenna's building are numbered 100 to 110. How many apartments on that floor are a prime number? What are those apartment numbers?
To find out how many apartments on the first floor are prime numbers, we need to check each apartment number from 100 to 110.
Prime numbers are numbers greater than 1 that are divisible only by 1 and themselves.
Let's check each apartment number:
Apartment 100: Not a prime number because it is divisible by 2.
Apartment 101: A prime number.
Apartment 102: Not a prime number because it is divisible by 2.
Apartment 103: A prime number.
Apartment 104: Not a prime number because it is divisible by 2.
Apartment 105: Not a prime number because it is divisible by 3 and 5.
Apartment 106: Not a prime number because it is divisible by 2.
Apartment 107: A prime number.
Apartment 108: Not a prime number because it is divisible by 2.
Apartment 109: A prime number.
Apartment 110: Not a prime number because it is divisible by 2 and 5.
So, there are a total of 4 apartments on the first floor that are prime numbers. The apartment numbers that are prime are: 101, 103, 107, and 109.
To find out how many apartments on the first floor are prime numbers, we need to check each apartment number from 100 to 110.
A prime number is a number that has exactly two distinct positive divisors: 1 and itself. So, we can check if each apartment number within the given range meets this criterion.
Starting from 100, we can check if it is divisible by any number other than 1 and itself. Dividing it by 2, we find that 100 is divisible by 2, meaning it is not a prime number.
We continue this process for each number within the range until we reach 110. Here is the breakdown:
100 ÷ 2 = 50 (Divisible by 2)
101 ÷ 2 = 50.5 (Not divisible by 2)
101 ÷ 3 = 33.67 (Not divisible by 3)
101 ÷ 4 = 25.25 (Not divisible by 4)
101 ÷ 5 = 20.2 (Not divisible by 5)
101 ÷ 6 = 16.83 (Not divisible by 6)
101 ÷ 7 = 14.43 (Not divisible by 7)
101 ÷ 8 = 12.63 (Not divisible by 8)
101 ÷ 9 = 11.22 (Not divisible by 9)
101 ÷ 10 = 10.1 (Not divisible by 10)
101 ÷ 11 = 9.18 (Not divisible by 11)
Since 101 has only two distinct positive divisors (1 and itself), it is a prime number.
110 ÷ 2 = 55 (Divisible by 2)
110 ÷ 3 = 36.67 (Not divisible by 3)
110 ÷ 4 = 27.5 (Not divisible by 4)
110 ÷ 5 = 22 (Divisible by 5)
110 ÷ 6 = 18.33 (Not divisible by 6)
110 ÷ 7 = 15.71 (Not divisible by 7)
110 ÷ 8 = 13.75 (Not divisible by 8)
110 ÷ 9 = 12.22 (Not divisible by 9)
110 ÷ 10 = 11 (Not divisible by 10)
110 ÷ 11 = 10 (Not divisible by 11)
Since 110 has more than two distinct positive divisors, it is not a prime number.
Therefore, among the apartment numbers 100 to 110, only 101 is a prime number.