Question

Find the average of all the factors of 60.

Answer 1

Hint: To solve this question we should have knowledge of what is average of factors of a number. The average of factor of a number is calculated by dividing the sum of all factors to the total number of factors, i.e. Average of factors of a number = (Sum of all factors / Total number of factors).

Complete step-by-step answer:
There are two types of numbers,
Prime numbers and composite numbers. We will first of all discuss them in detail.
Prime numbers – Prime numbers are the numbers that have only two factors 1 and themselves.
For example: 2, 3, 5, 7 etc.
Composite numbers – The numbers which are not prime are composite numbers. Also we can say that composite numbers are the numbers which have more than 2 factors.
Here we have to first find all factors of 60. Clearly 60 has more than 2 factors so it is a composite number.
All the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
So, there are a total of 12 factors of 60.
Average of factors of 60 = (Sum of all factors / Total number of factors).
\[\Rightarrow \] Average of factors of 60 = \[\dfrac{1+2+3+4+5+6+10+12+15+20+30+60}{12}\]
\[\Rightarrow \] Average of factors of 60 = \[\dfrac{168}{12}\].
\[\Rightarrow \] Average of factors of 60 = 14
Therefore the average of all factors of 60 is 14.

Note: Here the average of all factors of 60 is similar to calculating the mean of all factors of 60. If a question asked you to find the mean of all factors of 60 then also the calculation and answer would be the same.