If a1b1c1, a2b2c2, and a3b3c3 are three-digit even natural numbers and Δ=c1    a1    b1c2    a2    b2c3    a3    b3, then ∆ is

As a1b1c1, a2b2c2, and a3b3c3 are even natural numbers, each of c1, c2, c3 is divisible by 2. Let ci=2ki for i = 1, 2, 3. Thus,Δ=2k1    a1    b1k2    a2    b2k3    a3    b3=2mwhere m is some natural number. Thus, ∆ is divisible by 2.That ∆ may not be divisible by 4 can be seen by taking the three numbers as 112, 122, and 134. Note thatΔ=2    1    12    1    24    1    3=2which is divisible by 2 but not bY 4.