44, 96 and 184. when divided by a number x, leaves the same remainder in each case. The largest value of x is:

Correct option is B

Given:

Given numbers are 44, 96 and 184

Formula Used:

Formula Used:

Greatest number = HCF [(a-b), (b-c), (a-c)]

Where a, b, c are numbers and a > b > c

Solution:

Here 184 > 96 > 44

Hence HCF[(184 - 96),(96 - 44),(184 - 44)] = HCF[88, 52, 140]

Prime factorization of 88,52 and 140

88 = $$2^3 \times 11$$​​

52 = $$2^2 \times 13$$​​

140 = $$2^2 \times 5 \times 7$$​​

HCF = $$2^2 = 4$$​​