Introduction :

In Pattern theory, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. Patterns are common in many areas of mathematics. Recurring decimals are one example. These are repeating sequences of digits which repeat infinitely. For example, 1 divided by 81 will result in the answer 0.012345679... the numbers 0-9 (except 8) will repeat forever 1/81 is a recurring decimal. In this article we shall discuss about patterns and relationships.(Source: wikipedia).

**Divisors pattern relationships:**

Consider the number 30. Divide 30 by 3, the remainder value is zero. Therefore 3 is the divisor of 30. Likewise divide 30 by value 2; we will get the value zero as the remainder. Again 2 is the divisor 30. By apply the same procedure, 1, 4, 5, 6, 8, 12, 24, 30 are also divisors. Therefore the divisors of 30 are 1, 2, 3, 4, 5, 6, 8, 12, 24 and 30. Now, consider the number 11. What are the divisors of 11? Obviously value 1 and value 12 are the only divisors.

**Factor pattern** **relationship****s:**

The divisors of a number except one and the number itself (same number) are called the factors of that number.

Find the divisors and factors of (a) 10, (b) 30

**Solution:**

The divisors of 10 are 1, 2, 5, and 10

The factors of 10 are 2, 5

**Solution:**

The divisors of 30 are 1, 2, 5, 6, 15 and 30

The factors of 30 are 2, 5, 6 and 15

**Multiples pattern relationships:**

Consider the number 3

Multiplying 3 by the numbers 1, 2, 3 …

Therefore we get the values 3, 6, 9, 12, 15 ...these are multiples of 4.

**Example:**

Find six multiples of 6

**Solution:**

The five multiples of 6 are

1 × 6 = 6

2 × 6 = 12

3 × 6 = 18

4 × 6 = 24

5 × 6 = 30

The five multiples of 6 are 6, 12, 18, 24, 30

**Example:**

Find five multiples of 10

1 × 10 = 10

2 × 10 = 20

3 × 10 = 30

4 × 10 = 40

5 × 10 = 50

The five multiples of 10 are 10, 20, 30, 40, 50.

Consider the whole numbers they are multiples of 3

0 × 3, 1 × 3, 2 × 3, 3 × 3, 4 ×3,…

That is, 0, 3, 6, 9, 12 … these are multiples of 3.

Consider the whole numbers which are not multiples of 3

1, 2, 4, 5, ……………

The numbers which are multiples of 2 are said to be even **numbers**.

When the number divide by the even number by 2, the remains will be zero

The whole numbers are not multiple of 2 are said to be **odd numbers.**