What is the total prime numbers between 130 and 150 ?
The Correct Answer and Explanation is :
To find the total number of prime numbers between 130 and 150, we first need to understand what a prime number is. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number cannot be formed by multiplying two smaller natural numbers.
Identifying Prime Numbers between 130 and 150
We will check each number between 130 and 150 to see if it is prime:
- 131: The divisors to check are 2, 3, 5, 7, 11. None divide evenly into 131, so it is prime.
- 132: Even number (divisible by 2), not prime.
- 133: Divisible by 7 (133 = 7 × 19), not prime.
- 134: Even number, not prime.
- 135: Divisible by 5 (135 = 5 × 27), not prime.
- 136: Even number, not prime.
- 137: Check divisors up to √137 (approximately 11.7). None divide evenly, so it is prime.
- 138: Even number, not prime.
- 139: Check divisors up to √139 (approximately 11.8). None divide evenly, so it is prime.
- 140: Even number, not prime.
- 141: Divisible by 3 (141 = 3 × 47), not prime.
- 142: Even number, not prime.
- 143: Divisible by 11 (143 = 11 × 13), not prime.
- 144: Even number, not prime.
- 145: Divisible by 5 (145 = 5 × 29), not prime.
- 146: Even number, not prime.
- 147: Divisible by 3 (147 = 3 × 49), not prime.
- 148: Even number, not prime.
- 149: Check divisors up to √149 (approximately 12.2). None divide evenly, so it is prime.
Summary of Prime Numbers
The prime numbers identified between 130 and 150 are:
- 131
- 137
- 139
- 149
Conclusion
In total, there are four prime numbers between 130 and 150: 131, 137, 139, and 149. This exercise illustrates the systematic approach to identifying prime numbers within a specified range, emphasizing the importance of checking for divisibility against known prime numbers up to the square root of the target number.