Question

The sum of all those prime numbers which are less than 31 is
A.119
B.129
C.132
D.137

Answer 1

Hint: First of all, we will write all the factors of numbers less than 31. The numbers with only two factors are prime numbers. Hence, we will select all the prime numbers less than 31. Next, we will add all the prime numbers from 1 to 30 to get the required result.

Complete step-by-step answer:
We know that the prime numbers are those numbers which have only 2 factors, the factor 1 and the number itself.
We have to find the sum of all the prime numbers less than 31.
First of all, we will write all the prime numbers less than 31.
We shall write the factors of the numbers from 1 to 30.

Number	Factors
1	1
2	1,2
3	1,3
4	1,2,4
5	1,5
6	1,2,3,6
7	1,7
8	1,2,4,8
9	1,3,9
10	1,2,5,10
11	1,11
12	1,2,3,4,6,12
13	1,13
14	1,2,7,14
15	1,3,5,15
16	1,2,4,8,16
17	1,17
18	1,2,3,6,9,18
19	1,19
20	1,2,4,5,10,20
21	1,3,7,21

22	1,2,11,22
23	1,23
24	1,2,3,4,6,8,12,24
25	1,5,25
26	1,2,13,26
27	1,3,9,27
28	1,2,4,7,14,28
29	1,29
30	1,2,3,5,6,10,15,30

Here, the numbers with only two factors are prime numbers.
Hence, the prime numbers less than 31 are 2,3,5,7,11,13,17,19,23,29
We want to find the sum of the prime numbers which are less than 31.
That is, $2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129$
Hence, option B is correct.

Note: Factors of a number are those numbers which divide the number completely. The numbers with only two factors are prime numbers. The numbers with more than two factors are known as composite numbers. And 1 is neither a prime nor a composite number.