Understanding Prime Numbers
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Numbers that have more than two divisors are called composite numbers.
Analyzing the Options
We need to determine which of the given numbers is a prime number by checking their divisors.
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Option 1: 157
To check if 157 is prime, we test divisibility by prime numbers up to $\sqrt{157}$. Since $\sqrt{157} \approx 12.53$, we only need to check primes 2, 3, 5, 7, and 11.- 157 is not divisible by 2 (it is odd).
- The sum of digits $1+5+7=13$, which is not divisible by 3, so 157 is not divisible by 3.
- 157 does not end in 0 or 5, so it is not divisible by 5.
- $157 \div 7 \approx 22.43$ (remainder is 3). Not divisible by 7.
- $157 \div 11 \approx 14.27$ (remainder is 3). Not divisible by 11.
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Option 2: 121
$121 = 11 \times 11 = 11^2$. Since it has divisors other than 1 and itself (namely 11), 121 is not a prime number. -
Option 3: 1331
$1331 = 11 \times 11 \times 11 = 11^3$. Since it has divisors other than 1 and itself (namely 11), 1331 is not a prime number. -
Option 4: 81
$81 = 9 \times 9 = 9^2$ or $3 \times 3 \times 3 \times 3 = 3^4$. Since it has divisors other than 1 and itself (namely 3 and 9), 81 is not a prime number.
Conclusion
Based on the analysis, only 157 fits the definition of a prime number.
Similar Questions
- The number of prime numbers lying between 389 and 403, both included, is:
- The sum of the first four prime numbers is:
- In four consecutive prime numbers, the product of the last three is 7429 and that of the first three is 4199. The largest of these prime number is:
- How many of the integers between $109$ and $121$, both inclusive, are prime numbers?
- The sum of the first six prime numbers is:
- If $a : b = 3 : 4$ and $d : b = 4 : 3$, then find the ratio of a to d.
- Consider the following statements and decide which of them is/are correct.
1) Every prime is odd.
2) Product of any two prime numbers is odd. - Which of the following numbers is NOT prime?
- Which one of the following numbers is NOT a prime number?
- Which of the following numbers is prime?
Important Questions from Prime Numbers
Which of the following is NOT a pair of co-prime numbers?
a and b are two positive integers such that the least prime factor of a is 2 and the least prime factor of b is 5. Then the least prime factor of a + b is
Which of the following is a pair of coprime numbers ?
If product of two prime numbers A and B (A < B) is 221, then what is the value of (4A – 3B)?
Sum of all the prime numbers between 70 and 100 is :
