Question

What factors of \[24\] are prime numbers?

Answer 1

Hint:We need to know what actually prime numbers and factors are.
PRIME NUMBERS – The numbers which are divisible by \[1\] and itself only are the prime numbers.
FACTORS – The factors of a number are the numbers which divide the given number without leaving any remainder.
Now, In this question, we have to find which factors of \[24\] are prime factors. For that, first of all we need to find the factors of \[24\] and then we need to categorise them as prime numbers or composite numbers (The numbers whi

Complete step-by-step solution:
Finding out the factors of \[24\]
\[24\] can be written as:
\[
  24 = 1 \times 24 \\
  24 = 2 \times 12 \\
  24 = 3 \times 8 \\
  24 = 4 \times 6 \]
Therefore, factors of \[24\] are: \[1,2,3,4,6,8,12,24\].
Now, we need to categorise the factors as prime or composite.
\[1\] is divisible by \[1\] only.
\[2\]is divisible by \[2\] and \[1\] only.
\[3\]is divisible by \[3\] and \[1\] only.
\[4\]is divisible by \[1,2,4\].
\[6\]is divisible by \[1,2,3,6\].
\[8\]is divisible by \[1,2,4,8\].
\[12\]is divisible by \[1,2,3,4,6,12\].
\[24\]is divisible by \[1,2,3,4,6,8,12,24\].
We see that only \[1,2and3\] are the numbers which are divisible by \[1\]and itself.
Also, we know that \[1\] is neither prime nor composite.
Therefore, the factors of \[24\] which are prime are \[2\] and \[3\].

Note: We need to keep in mind that we should not include \[1\] in prime numbers. \[1\] is neither prime nor composite. Also, we need to make sure that \[1\] is included in the factors also. We usually forget to consider \[1\] and the number itself as the factors of the number. We should be very careful while categorising the numbers as prime or composite. We know, a number is at least divisible by \[1\] and the number itself. So, we need to add them while counting the divisible numbers for a number.