# Playing with Numbers

## Playing with Numbers

### General Form of Numbers

Various types of numbers such as Natural numbers, Whole numbers, Integers, Rational numbers and the various properties such as closure, associative, commutative and distributive.

2-digit number
The number in the general form can be written as for example 26 = 2 x 10 + 6. General Form of a 2-digit Number 10 × a + 1 × b
1. The sum of a 2-digit number and the number obtained by interchanging its digits is always divisible by 11.
2. The difference between a 2-digit number and the number obtained by interchanging its digits is always divisible by 9.

Assume ab is a 2-digit number.
•  a is the tens digit
•  b is the ones digit

ab = 10 × a + 1 × b.

3-digit number
General form of a 3-digit number is 100 × a + 10 × b + 1 × c.

1. The difference between a 3-digit number and a number obtained by reversing its digits is always divisible by 99.

Assume abc is a 3-digit number, where:
•  a is the hundreds digit
•  b is the tens digit
•  c is the ones digit

abc = 100 × a + 10 × b + 1 × c

Letters for digits
Assume that each letter in a puzzle stands for just one digit and each digit is represented by a one letter, so it is like cracking a code. Here problems of addition and multiplication to solving puzzles.

For example, eighty one will be written as 81 not as 081 or 0081.

### Tests of Divisibility

The tests of divisibility with 10, 5, 2, 3, 6, 4, 8, 9 and 11. In this, learn why the numbers are divisible by 10, 5, 2, 3, 6, 4, 8, 9 and 11.
A number is said to be divisible by another number, when the remainder is zero.

•  A number is divisible by 10, if its ones digit is 0.

•  A number is divisible by 5, if its ones digit is 0 or 5.

•  A number is divisible by 2, if its ones digit is 0, 2, 4, 6 or 8.

•  If a number is divisible by 10, then the number is also divisible by 2 and 5.

•  A number is divisible by 9, if the sum of its digits is divisible by 9.

•  A number is divisible by 3, if the sum of its digits is divisible by 3.

•  If a number is divisible by 9, then the number is also divisible by 3.

•  If a number is divisible by 3, then it may not necessarily be divisible by 9.

•  If a number is divisible by 6, then the number is divisible by 2 as well as 3.

•  If a number is divisible by 11, then the difference of its digits in odd places and the sum of its digits in
even places is either 0 or a multiple of 11.

•  If a number is divisible by 4, then the number formed by its digits in units and tens places is divisible by 4.