 What are the 8 Types of Numbers? | Maths Grade 5 | ORCHIDS Numbers

Types of Numbers

We can classify numbers in different groups based on their properties.

Natural Numbers

All the counting numbers are known as Natural Numbers.

Example: {1, 2, 3, 4, 5, 6, ……………………………………}

We denote the collection of all the natural numbers by .

Whole Numbers

All the natural numbers and the number 0 are known as Whole Numbers.

Example: {0, 1, 2, 3, 4, 5, 6, ……………………………………}

We denote the collection of all the whole numbers by 𝕎.

• All natural numbers are whole numbers. But all whole numbers are not natural numbers, since 0 is a whole number but not a natural number. There are also some other types of the numbers:

Even Numbers

The numbers which have digit 0, 2, 4, 6 or 8 at its Ones place are called Even numbers.

(Numbers ends with 0, 2, 4, 6, or 8)

Examples:

```45,780              2,708              3,35,034              926
```

Operations on even numbers

1. Sum of two even numbers is always an even number.

Example: 68 and 72 are even numbers.

68 + 72 = 140 → 140 is an even number.

2. Difference between two even numbers is always an even number.

Example: 98 and 54 are even numbers.

98 – 54 = 44 → 44 is an even number.

3. Product of two even numbers is always an even number.

Example: 42 and 8 are even numbers.

42 × 8 = 336 → 336 is an even number.

4. Even numbers are always divisible by 2.

Example: 54, 78, 12, 20, 6 all are even numbers. And all these numbers are divisible by 2. Means when we divide these numbers by 2, we get 0 as remainder. Odd Numbers

The numbers which have digit 1, 3, 5, 7 or 9 at its Ones place are called Odd numbers.

(Numbers ends with 1, 3, 5, 7, or 9)

Examples:

2,783 87,617 6,20,039 225

Operations on odd numbers

1. Sum of two odd numbers is always an even number.

Example: 87 and 25 are odd numbers.

87 + 25 = 112 → 112 is an even number.

2. Difference between two odd numbers is always an even number.

Example: 75 and 13 are odd numbers.

75 – 13 = 62 → 62 is an even number.

3. Product of two odd numbers is always an odd number.

Example: 15 and 7 are odd numbers.

15 × 7 = 105 → 105 is an odd number.

Operations with even and odd numbers Prime Numbers

The numbers which are divisible by only 1 and itself are called Prime Numbers.

Example:

2, 3, 5, 7, 11, 13, etc. are prime numbers.

2 = 1 × 2 3 = 1 × 3 5 = 1 × 5

7 = 1 × 7 11 = 1 × 11 13 = 1 × 13

We can see that, all the above numbers have only two factors.

• Prime number has only two factors 1 and that number itself.
• Smallest prime number is 2.
• All the prime numbers are odd numbers except 2. 2 is the only even prime number.

Composite Numbers

The numbers which are divisible by at least one number other than 1 and itself are called Composite Numbers.

Example:

4, 6, 8, 10, 12, 14, etc. are composite numbers. We can see that, all the above numbers have more than two factors.

• Composite number has more than two factors.
• Smallest composite number is 4.
• 0 and 1 are neither prime nor composite.

Co-prime Numbers

The pair of numbers that have only one common factor as 1 are called Co-prime Numbers. These are also called relatively prime numbers.

Example:

28 and 57 are co-prime numbers. Only common factor is 1.

Twin prime numbers

Two prime numbers whose difference is 2 are called twin prime numbers.

Example:

(3, 5), (11, 13), (107, 109), etc. are twin prime numbers. We can see that, in the above examples, difference between prime numbers is 2.

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