Choose the composite numbers from the following numbers: 87,67,45,34,23,27,33.
A) 45,87,34,27,33
B) 45,87,67,33
C) 33,27,23,34
D) All of the above
E) None of these

Hint: According to the definition of composite number, a number which has factors other than 1 and the number itself, are called composite numbers. While, the numbers which have factors either 1 or the number itself are called prime numbers. So, to choose the composite numbers from the given numbers we simply need to factorize the numbers and check for the factors.

Complete step by step answer:
For a number to be composite, its factors should be different from 1 and the number itself. So we will factorize all the numbers one by one and choose the composite numbers accordingly.
Now, starting with the first number 87. Factorising 87 will give us the factors as
$87 = 3 \times 29$ which are different from 1 and 87. So, 87 is a composite number.

Next we factorize the second number 67. Factorising 67 will give us the factors as
$67 = 1 \times 67$ that is, the only factors are 1 and the number itself 67. Hence 67 is a prime number and not a composite number.

Next we factorize the third number 45. Factorising 45 will give us the factors as:
$45 = 3 \times 3 \times 5$ which are different from 1 and the number itself. Hence 45 is a composite number

Next we factorize the fourth number 34. Factorising 34 will give us the factors as:
$34 = 2 \times 17$ which are different from 1 and the number itself. Hence 34 is a composite number

Next we factorize the fifth number 23. Factorising 23 will give us the factors as:
$23 = 1 \times 23$ that is the only factors are 1 and the number itself 23. Hence 23 is a prime number and not a composite number.

Next we factorize the sixth number 27. Factorising 27 will give us the factors as:
$27 = 3 \times 3 \times 3$ which are different from 1 and the number itself. Hence 27 is a composite number

Next we factorize the seventh number 33. Factorising 33 will give us the factors as:
$33 = 3 \times 11$ which are different from 1 and the number itself. Hence 33 is a composite number
Therefore, out of the given numbers, 87,45,34,27 and 33 are composite numbers because they have factors which are different from 1 and the number itself.

Hence the correct answer is option A.

Note: The consideration of factors determines whether the number is composite or not. So, it has to be done very carefully and we have to check every possibility before confirming it with the composite or prime numbers.