Let's analyze the given list of numbers step-by-step to answer the questions provided.
Given list of numbers:
[tex]\[ 13, 27, 81, 21, 43, 48, 23, 39, 45 \][/tex]
### a) Finding the even number.
An even number is a number that is divisible by 2.
Going through the list:
- 13 (odd)
- 27 (odd)
- 81 (odd)
- 21 (odd)
- 43 (odd)
- 48 (even - divisible by 2)
- 23 (odd)
- 39 (odd)
- 45 (odd)
So, the even number in the list is:
[tex]\[ 48 \][/tex]
### b) Finding the square number.
A square number is a number that can be expressed as the square of an integer.
Analyzing the list:
- 13 (not a square of any integer)
- 27 (not a square of any integer)
- 81 (9 x 9, square of 9)
- 21 (not a square of any integer)
- 43 (not a square of any integer)
- 48 (not a square of any integer)
- 23 (not a square of any integer)
- 39 (not a square of any integer)
- 45 (not a square of any integer)
So, the square number in the list is:
[tex]\[ 81 \][/tex]
### c) Finding all the prime numbers.
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
Analyzing each number:
- 13 (prime, divisible only by 1 and 13)
- 27 (not prime, divisible by 1, 3, 9, 27)
- 81 (not prime, divisible by 1, 3, 9, 27, 81)
- 21 (not prime, divisible by 1, 3, 7, 21)
- 43 (prime, divisible only by 1 and 43)
- 48 (not prime, divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48)
- 23 (prime, divisible only by 1 and 23)
- 39 (not prime, divisible by 1, 3, 13, 39)
- 45 (not prime, divisible by 1, 3, 5, 9, 15, 45)
So, the prime numbers in the list are:
[tex]\[ 13, 43, 23 \][/tex]
In summary:
a) The even number is [tex]\( 48 \)[/tex].
b) The square number is [tex]\( 81 \)[/tex].
c) The prime numbers are [tex]\( 13, 43, 23 \)[/tex].
