Question

The prime factors of the denominator of the fraction $\dfrac{3}{{80}}$ are
A) 5 and 8
B) 2 and 5
C) 2,4 and 5
D) 1,7 and 5

Answer 1

Hint: In this question, we have a denominator in the fraction as 80. It is a composite number and not the prime number. We have to find its factors. For factorization take the numbers without repetition which are the prime factors of 80. Remember that complete fraction will not be considered for factorization here.

Complete step-by-step answer:
In the given fraction $\dfrac{3}{{80}}$ , 80 is the denominator.
As we know that 80 is a composite number. So, it will have prime factors except 1 and itself.
Now, we will find its pair of factorization, as follows,
$80 = 1 \times 80$
Next we do factorization of 80 as,
$
  80 = 1 \times 80, \\
  80 = 2 \times 40 \\
 $
Next we do factorization of 40 as,
$80 = 4 \times 20,$
In this way further, we get
$
  80 = 4 \times 20, \\
  80 = 5 \times 16, \\
  80 = 8 \times 10, \\
 $
Thus all factors of 80, by using above mentioned multiplication method, as bellow
Factor of \[80:1,2,4,5,8,10,16,20,40,80\]
And also, \[{\text{factorisation}}\;{\text{of}}\;{\text{80}}\;{\text{:2}} \times {\text{2}} \times {\text{2}} \times {\text{2}} \times {\text{2}} \times {\text{5}}\]
Which can be also written as , \[80 = {2^4} \times 5\]
$\therefore $ We can see that prime factors of 80 are 2 and 5, after elimination of the repetitions.

Thus option (2) is correct.

Note: 1. The fraction in math represents the equal parts of a whole value. When we divide a whole value into equal parts, then each part will be a fraction of the whole.
2. The top number in the fraction is termed as the numerator. And the bottom number is termed denominator. The numerator represents how many parts we have, whereas the denominator represents how many total equal parts are there.
3. A factor is a prime number and if the factors are multiplied with each other, the original number can be obtained. For example, prime factors of 20 are 2 and 5 without repetition.