Number System - Online Test

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264  11,3,4 (/)

396  11,3,4 (/)

462  11,3 (X)

792  11,3,4 (/)

968  11,4 (X)

2178  11,3 (X)

5184  3,4 (X)

6336  11,3,4 (/)

Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

Required number of number = 4.

935421 x 625 = 935421 x 54 = 935421 x		10		4
		2

= 584638125

Largest 4-digit number = 9999

 88) 9999 (113
     88
     ----
     119
      88
     ----
      319
      264
      ---
       55
      ---
       
 Required number = (9999 - 55)
                 = 9944.

Unit digit in (6374)¹⁷⁹³ = Unit digit in (4)¹⁷⁹³

    = Unit digit in [(4²)⁸⁹⁶ x 4]

    = Unit digit in (6 x 4) = 4

Unit digit in (625)³¹⁷ = Unit digit in (5)³¹⁷ = 5

Unit digit in (341)⁴⁹¹ = Unit digit in (1)⁴⁹¹ = 1

Required digit = Unit digit in (4 x 5 x 1) = 0.

Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

Let the smaller number be x. Then larger number = (x + 1365).

 x + 1365 = 6x + 15

 5x = 1350

 x = 270

Smaller number = 270.