- 
					 If in a long division sum,the dividend is 380606 and the successive remainders from the first to the last are 434, 125 and 413, then the divisor is ?
- 
                        - 451
- 843
- 4215
- 3372
 
Correct Option: B
Let d = divisor and q = quotient 
First remove the last remainder: 
d x q + 413 = 380606 
d x q = 380193 
So d cannot be even (choice d) or a multiple of 5 (choice c). 
If we try choice a or b, 
a quick division (by calculator) shows that 
380193 = 451 x 843, the other two choices. 
(In the absence of choices, we could find the prime factors of 380193, 
which are 3 x 11 x 41 x 281 and get various candidate divisors from that.) 
So one of them is the divisor and the other the quotient. 
So we can just check the first remainder: 
843 x 4 = 3372 
3806 - 3372 = 434 ... a match! 
And just to be sure: 
451 x 8 = 3608 
3806 - 3608 = 198 
So the divisor is 843. 
 
	