Introduction for Solving Number Patterns

Solving number patterns is the main topic under the solving number systems. In this lesson we have to study about the concepts of divisors, factors, multiples and prime numbers. Also in this topic we have to discuss about properties of number patterns. Here we have to discuss about Divisors, Factors ,Multiples,Even,Odd numbers,Prime numbers and Composite numbers. These are the main topics in the solving number patterns.

Solving Divisors, Factors and Multiples Number Patterns:

Divisors:

Step 1: Consider the number 96. Divide 96 by 4. When we divide 96 by 4, the remainder is 0.

Step 2: 4 is the divisor of 96. Similarly if we divide 96 by 2, we will get 0 as the remainder.

Step 3: Again 2 is the divisor 96. By applying the same process, 1,2,3,4,6,8,12,16,24,32,48,96 are also divisors.

Step 4: Thus the divisors of 96 are 1,2,3,4,6,8,12,16,24,32,48,96.

Note:

The divisor in the division algorithm is different from this divisor. In division algorithm the divisor indicates the denominator only.

Example:

Find the divisors of (a) 28, (b) 35

Solution:

(a) Solving The divisors of 28 are 1, 2, 4,7,14, and 28

(b) Solving The divisors of 35 are 1, 5, 7 and 35

Solving even and Odd Number Patterns and Prime and Composite Patterns:

The numbers that are divisible by 2 is called as even numbers.
If we divide the even number by 2, the remainder is always zero.

The numbers that are not divisible by 2 is called as odd number.
If we divide an odd number by 2, the remainder is always 1

Now observe the following:

(a) 2 + 2 = 4 ; 2 + 6 = 8 ; 4 + 8 = 12 ; 10 + 20 = 30

(b) 2 × 2 = 4 ; 2 × 6 = 12 ; 4 × 8 = 32 ; 10 × 20 = 200

From the above examples the following are true.

Even number + even number = even number
Even number × even number = even number
Odd number + odd number = even number
Odd number × odd number = odd number
These are the main rules used for solving number patterns.

Prime numbers and Composite number patterns

From the above, find the numbers that have only 2 divisors?

2, 3, 5 and 7 have only two divisors.

What are the numbers which have more than 2 divisors?

4, 6, 8, 9 and 10 have more than 2 divisors.

The natural numbers that have only two divisors are known as the prime numbers.
The natural numbers that have more than two divisors are known as the composite numbers.

Example:

Solving prime numbers between 20 and 30.

Solution:

The numbers between 20 and 30 are

21 22 23 24 25 26 27 28 29

∴ the prime numbers are 23 and 29