Integer Review: Fundamentals of Integers , Rules for Multiplication , Rules for divisibility, Division Terminology, Even & Odd Integer, Rules about even & odd integer, Prime Number, Prime Factorization , Distinct Prime Number, LCM & HCF, Composite Numbers , Consecutive Integers
Class Questions : Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5
Practice Questions : Solutions
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Prime Numbers
An integer which is greater than 1 and has only two divisors: the number itself and 1, is known as prime number. Following is table of prime numbers from 1 to 100. This is very important table, just review it thoroughly.
| Range |
Prime Numbers |
| 1 to 10 |
2, 3, 5, 7 |
| 11 to 20 |
11, 13, 17, 19 |
| 21 to 30 |
23, 29 |
| 31 to 40 |
31, 37 |
| 41 to 50 |
41, 43, 47 |
| 51 to 60 |
53, 59 |
| 61 to 70 |
61, 67 |
| 71 to 80 |
71, 73, 79 |
| 81 to 90 |
83, 89 |
| 90 to 100 |
97 |
|
|
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“1” is not a prime number.
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“2” is the only number which is even and prime.
Prime Numbers from 101 to 200:
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.
Prime Numbers from 201 to 300:
211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293.
Prime Numbers from 301 to 400:
307, 311, 313, 317, 331, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397.
Prime Numbers from 401 to 500:
401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.
Prime Factorization
If we break down any integer up to its prime number stage is called as Prime Factorization.
e.g.
Prime factorization of 24, 25, 58, 65, 99 and 12 will be;
24 = 2 x 2 x 2 x 3
25 = 5 x 5
58 = 2 x 29
65 = 5 x 13
99 = 3 x 3 x 11
12 = 2 x 2 x 3
Distinct Prime Number
The ‘Distinct Primes” are the numbers after prime factorization of any integer and consider it only once. That means same digit should not be repeated. Each prime digit will be counted only once.
Example1:
Find the distinct prime numbers of 48?
Solution;
The prime factorization of 48 = 2 x 2 x 2 x 2 x 3
So, Distinct Primes are 2 and 3 only. Though 2 is repeated here 4 times but take or count it only once.
Example 2:
Find the sum of distinct primes of 225?
Solution;
The prime factorization of 225 = 5 x 5 x 3 x 3
So, Sum of Distinct Primes of 225 = 5 + 3 = 8.
The answer is = 8.
