Odd Numbers 1 to 400

Odd numbers can be classified into two types: composite odd numbers and consecutive odd numbers. The numbers that have factors more than two and greater than 1 are called composite numbers.

When a composite number is not divisible by 2, it is called a composite odd number. For example, 9, 15, and 21 are composite odd numbers.

The pair of odd numbers that have a difference of 2 are called consecutive odd numbers. For example, 3 and 5 are consecutive odd numbers.

Odd numbers follow these properties:

- Odd numbers always end with 1, 3, 5, 7, or 9.

- When you add two odd numbers, the result is always an even number.

- Multiplying two odd numbers always gives another odd number.

- The square of any odd number is always an odd number.

The pictorial representation helps children learn odd numbers easily.

By using this chart, children can know the sequence and series of numbers.

Let’s take a look at the odd number chart, ranging between 1 and 400.

Odd numbers are not divisible by the number 2. To find odd numbers, we can use the formula: \(2n + 1\) where \(n\) is an integer. For example, if \(n = 2\) then \(2n + 1 = 2(2) + 1 = 4 + 1 = 5\), which is an odd number.

1. Squaring an odd number, meaning multiplying an odd number by itself, always gives an odd number. For example, the square of 5 is 5 x 5 = 25\), which is an odd number.

2. When you add odd numbers starting from 1, the total becomes a perfect square. For example, adding odd numbers from 1 to 7: \(1 + 3 + 5 + 7 = 16\), which is a perfect square.

3. Prime numbers are the numbers that have only two factors: 1 and the number itself. Let’s take a look at a list of odd numbers from 1 to 400: 1, 3, 5, 7, 9, 11, 13, 15, 17, .............., 381, 383, 385, 387, 389, 391, 393, 395, 397, 399.

For the sum of odd numbers, a simple formula is used - Sum of odd numbers = \(n²\) Here, \(n = 200\) because there are 200 odd numbers from 1 to 400.

Substitute \(n = 200\) into the formula, we get The sum of odd numbers from 1 to 400 = \(200² = 40000\)

When you subtract one odd number from another, the result is always an even number.

Odd – Odd = Even Example: 15 – 7 = 8 From the above example, 15 and 7 are odd numbers. When we subtract 7 from 15, we get 8, which is an even number. 

Odd Prime Numbers 1 to 400  The positive numbers having exactly two factors, 1 and themselves, are called prime numbers.

The prime numbers which are not divisible by 2 are called odd prime numbers. All prime numbers other than 2 are odd numbers. Example for odd prime numbers: 3, 5, 7, 11, 13,.........

A few points to remember for odd numbers are as follows: - The smallest odd prime number is 3. - Excluding 2, all prime numbers are odd. - The smallest positive odd number is 1. - 40000 is the total of all odd numbers from 1 to 400.

• Composite numbers: The numbers greater than 1, having more than two factors, are called composite numbers. Example: 9 is a composite number because it is divisible by 1, 3, and 9.

• Perfect square: It is a number that is the product of a number multiplied by itself. Example: 25 is a perfect square number because it is obtained by multiplying 5 with 5 \(5 x 5 )\).

• Odd prime numbers: The prime numbers that are not divisible by 2 are called odd prime numbers. Example: 5 is an odd prime number because 5 is a prime number, and it is not divisible by 2.

• Arithmetic sequence: A sequence of numbers in which the difference between any two consecutive numbers is always the same. Example: 3, 7, 11, 15 is an arithmetic sequence with a common difference of 4.

• Consecutive odd numbers: A pair of odd numbers where the difference is 2. Example: 5 and 7 are consecutive odd numbers.