This post contains the funs and facts of Prime Numbers, Composite Numbers, Co-prime Numbers and important Question-Answers for all competitive viewers and New children who try to know the mathematics in easy way.
Prime Number:
Prime Numbers are the selective natural numbers that are divisible by one (1) and itself. Each and every prime number has only two factors one and itself. Prime numbers are positive natural number. 1 is not a prime number.
Prime Number: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ………
Magical funs and facts of prime numbers:
- 1is not a prime number but it is a natural number and whole number.
- 2 is the smallest prime number and even prime number.
- Except 2, all prime numbers are odd prime numbers.
- Every two prime numbers are always co-prime numbers of each other.
- All 25 prime numbers between 1 and 100.
- All 15 prime numbers between 1 and 50.
- All 10 prime numbers between 50 and 100.
- Only two consecutive natural numbers are prime number i.e. 2 and 3.
How to find the prime numbers?
Prime Numbers are the multiple of 6 and either add 1 or subtract 1.
Here, 6n+1
Rule: To check a number is a prime number or not?
We get a number 503.
503 + 1= 504; Either 504 is divisible by 6, then it is a prime number
Or
503 – 1 = 502; 502 is divisible by 6, then it is a prime number
So, 504 is divisible by 6. Hence, 503 is a prime number
Most favourable funs and facts of prime numbers are between 1 and 100
| 2 | 2 |
| 3 | 3 |
| 5 | 6×1-1 |
| 7 | 6×1+1 |
| 11 | 6×2-1 |
| 13 | 6×2+1 |
| 17 | 6×3-1 |
| 19 | 6×3+1 |
| 23 | 6×4-1 |
| 29 | 6×5-1 |
| 31 | 6×5+1 |
| 37 | 6×6+1 |
| 41 | 6×7-1 |
| 43 | 6×7+1 |
| 47 | 6×8-1 |
| 53 | 6×9-1 |
| 59 | 6×10-1 |
| 61 | 6×10+1 |
| 67 | 6×11+1 |
| 71 | 6×12-1 |
| 73 | 6×12+1 |
| 79 | 6×13+1 |
| 83 | 6×14-1 |
| 89 | 6×15-1 |
| 97 | 6×16+1 |
Composite Number:
Composite Numbers are the natural numbers that have more than two factors are called the composite numbers. Composite Numbers must have at least one more factor except 1 and itself. 1, 2 and 3 are not a composite number.
Composite Number: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21,…………
How to find the composite number?
| Example: To check 15 is a composite number or not? |
| Let find the factor of 15 |
| 1 x 15 =15 |
| 3 x 5 =15 |
| 5 x 3 = 15 |
| 15 x 1 =15 |
| There are two more factors of 15 is 3 and 5 except 1 and itself 15. |
| Hence, 15 is Composite Number. |
Type of composite number
| Even Composite Number: All the even natural numbers that have at least one more factor except 1 and itself. In other word, those even numbers are not a prime number is known as Even Composite Number. Example: 4, 6, 8, 10, 12………… |
| Odd Composite Number: All the odd natural numbers that have at least one more factor except 1 and itself. In other words, those odd numbers are not a prime number is known as Odd Composite Number. Example: 9, 15, 21, 25, 27, 33, 35, 39…………… |
Magical funs and facts of composite numbers:
| # 0, 1, 2 and 3 are not a composite number. # It has at least one more factor except 1 and itself. # Each and every composite number is a factor of itself. # The smallest composite number is 4. # The first squared composite number is 4. # Each and every composite number has prime factor. |
Co-prime Number:
Co-prime Numbers are always in a pair that have only one common factor for both. A pair of numbers are said to be co-prime number that have highest common factor (HCF) is 1. Each number of a pair is the co-prime number of other number. Co-prime Number: (2,3), (3,5), (5,7), (1,2), (5,6), (4,9), (3,10), (3,11)…….
How to find the co-prime number?
| Example: To check a pair (4,9) is a co-prime number or not? |
| Find the factors of 4. |
| 1 x 4 = 4 |
| 2 x 2 = 4 |
| 4 x 1 = 4 |
| There are three factors of 4. i.e. 1, 2, 4 |
| Find the factors of 9. |
| 1 x 9 = 9 |
| 3 x 3 = 9 |
| 9 x 1 = 9 |
| There are three factors of 9. i.e. 1, 3, 9 |
| Hence, |
| The highest common factor (HCF) is 1 |
| So, (4,9) is a co-prime number. |
Magical funs and facts of co-prime numbers:
| # Two successive numbers are always co-prime number. (9,10), (15,16)…. |
| # 1 is co-prime of every number |
| # Any two prime number is always co-prime number of each other. |
| The sum of two co-prime number and their product is always a co-prime number. # Let check, (5,6) is a co-prime number? # The sum = 5 + 6 =11 and their product = 5 x 6 = 30 # The factors of 11 are 1 and 11 # The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 # Hence, The highest common factor is 1. # So, (11, 30) is a co-prime number. |
Lets do some fun with prime numbers and co-prime numbers?
Q: To check the following numbers are prime numbers or not?
| # 571 # 783 # 789 # 971 # 567 |
Q: To circle the prime numbers?
| # 345 # 673 # 679 # 371 # 981 |
Q: To check the following pairs are co-prime number or not?
| # (28, 57) # (41, 75) # (10, 30) # (18, 35) # (45, 100) |
For General Knowledge: General Knowledge || Decimal Number System