B)

Find the greatest number which divides 323, 539 and 827 leaving remainder 35

each case

greatest number is 72

Step-by-step explanation:

Given 323, 539 and 827

we will use remainder theorem

f (x) (dividend) = d (x) (divisor). q (x) (quotient) + r (x) (remainder)

given data which divides 323,539 and 827 leaving remainder '35'

323-35 = 288

539-35 = 504

827-35 = 792

now find all factors of these resulting numbers

288 = 2^5 X 3^2

504 = 2^3 X 3^2 X7

792 = 2^3 X 3^2 X11

all these take common factors is 2^3 X 3^2 = 8 X9 = 72

There fore the greatest number of given data is 72.