prime numbers

To know the prime factors, it is better to get the number, so the core of the problem is to calculate S, the sum of integers from 30 to 50

I use the formula
"the sum for i=0 to n" of i= n(n+1)/2

A="the sum for i=0 to 50" of i = 50*51/2=1275
B="the sum for i=0 to 29" of i = 29*30/2=435

Now to get S we need to do add A and subtract all the members we do not want, namely B
S=A-B=1275-435=840

Now, it's ok
840=2.2.2.3.5.7

There are 4 different prime factors.

I go with D .4

sum of all numbers from 30 to 50 is
n = 50-30+1 = 21

21/2(30+50)=840

840 can be written as 12*7*10
= 3*4 * 7*5*2 hence 4 different prime factors..

Hope it helps..

Sum of consecutive integers from 30 to 50
= Total number of terms/2 * Sum of (first and last term)

Total number of terms = (50 -30) + 1 = 21

Sum = 21/2 * (50 +30) = 840

factors of 840 = (2**3) * 3 * 5 * 7

Number of prime factors = 2, 3, 5, 7 (4)