Various Types of Numbers

In various types of numbers we will learn about even numbers, odd numbers, prime numbers, composite numbers, co-prime numbers and twin prime numbers along with the example.

Even Numbers:

A whole number exactly divisible by 2 is called even numbers.

A whole number which is exactly divisible by 2 is called an even number. The collection (or set) of even numbers may be denoted by the letter E. Thus:

E = {0, 2, 4, 6, 8, 10, 12, ...}

For example:

2, 4, 6, 8, 10, 12, 14, 16..........................are even number. Or a number having 0, 2, 4, 6, 8 at its units place is called an even number.

246, 1894, 5468, 100 are even number.

Consecutive even numbers:

Any two even numbers which differ from one another by 2 are called consecutive even numbers.

Odd Numbers:

A whole number which is not exactly divisible by 2 is called an odd number.

Odd numbers A natural number which is not exactly divisible by 2 is called an odd number. The collection (or set) of odd numbers may be denoted by the letter O. Thus: O = {1, 3, 5, 7, 9, 11, 13, 15, ...}

For example:

3, 5, 7, 9, 11, 13, 15, are odd number.

Or, a number having 1, 3, 5, 7 and 9 at its units place is called an odd number.

Prime Numbers:

Numbers which have only two factors namely 1 and the number itself are called prime numbers.

Natural numbers (greater than 1) which have only two factors, viz., 1 and the number itself, are called prime numbers.

For example:

2, 3, 5, 7, 11, 13, 17, 19, 23, etc., are all prime numbers.

✅ The number 1 has only one factor. Hence, it is neither prime nor composite.

✅ 2 is the smallest prime number.

✅ 2 is a prime number as well as even.

✅ Every prime number except 2 is odd.

Composite Numbers:

Numbers having more than two factors are called as composite numbers.

Numbers which have more than two factors are called composite numbers. 

For example:

4, 6, 8, 9, 10, 12, etc., are composite numbers.

Notes:

(a) 1 is neither prime nor composite.

(b) 2 is the lowest and the only even prime number.

(c) 9 is the lowest odd composite number.

Co-prime Numbers:

Two numbers are said to be co-prime if they do not have a common factor other than 1 or two numbers whose HCF is 1 called co-prime numbers.

Two whole numbers are said to be co-primes, if they have no common factors other than 1. 

Two prime numbers are always co-primes.

Two co-primes need not be prime numbers.

Co-prime numbers needs not be prime numbers.

For example:

(i) 2 and 3 are co-prime.

(ii) 5 and 7 are co-prime.

(iii) 10 and 21 are co-prime.

(ii) 15 and 17 are co-prime.

Twin Prime Numbers:

Twin prime numbers are the two prime numbers whose difference is 2.

Two-primes Two consecutive odd prime numbers are known as twin-primes.

For example:

(i) 3 and 5

(ii) 17 and 19

(iii) 41 and 43

(iv) 29 and 31

(v) 71 and 73.

or, 

For example, (3, 5); (5, 7); (11, 13); (17, 19); (29, 31); (41, 43); (59, 61); (71, 73), etc., are win-grimes.

Prime-Triplet:

A set of three consecutive prime numbers, differing by 2, is called a prime pet.

For example:

(3, 5, 7) is a prime triplet.

Perfect Numbers:

If the sum of all the factors of a number is twice the number, the number is called a perfect her.

For example: 6 is a perfect number.

Factors of 6 are 1, 2, 3 and 6.

Sum of the factors = 1 + 2 + 3 + 6

                            = 12.

Twice times of 6 = 2 × 6 = 12.

5th Grade Math Problems

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