Question

Show that 527 + 752 + 275 is exactly divisible by 14.

Answer 1

Property:

abc = 100a + 106 + c ………(i)

bca = 1006 + 10c + a ……..(ii)

and cab = 100c + 10a + b ……….(iii)

Adding, (i), (ii) and (iii), we get abc + bca + cab = 111a + 111b + 111c = 111(a + b + c) = 3 x 37(a + b + c)

Now, let us try this method on
527 + 752 + 275 to check is it exactly divisible by 14

Here, a = 5, 6 = 2, c = 7
527 + 752 + 275 = 3 x 37(5 + 2 + 7) = 3 x 37 x 14

Hence, it shows that 527 + 752 + 275 is exactly divisible by 14.