Answer :
To determine which number among the given options is a prime number, let's analyze each one:
1. Number 60:
- A number is prime if it has no positive divisors other than 1 and itself.
- 60 is an even number and can be divided by 2.
- It can also be divided by other numbers such as 3, 4, 5, and 6.
- Therefore, 60 is not a prime number.
2. Number 59:
- Let's see if 59 can be divided by any other number apart from 1 and 59 itself.
- 59 is not divisible by 2 (since it is odd).
- The sum of the digits (5 + 9) equals 14, which is not divisible by 3, so 59 is not divisible by 3.
- It does not end in 0 or 5, so it's not divisible by 5.
- Checking divisibility by 7: \(59 \div 7 \approx 8.4285\) which is not a whole number.
- Thus, 59 is not divisible by any number other than 1 and 59.
- Therefore, 59 is a prime number.
3. Number 70:
- 70 is an even number (divisible by 2).
- It can also be divided by 5 (since it ends in 0).
- Therefore, 70 is not a prime number.
4. Number 96:
- 96 is also an even number (divisible by 2).
- It can be divided by multiple numbers such as 3, 4, 6, 8, and 12.
- Therefore, 96 is not a prime number.
After evaluating the given numbers, we find that the only prime number among them is:
B. 59.
1. Number 60:
- A number is prime if it has no positive divisors other than 1 and itself.
- 60 is an even number and can be divided by 2.
- It can also be divided by other numbers such as 3, 4, 5, and 6.
- Therefore, 60 is not a prime number.
2. Number 59:
- Let's see if 59 can be divided by any other number apart from 1 and 59 itself.
- 59 is not divisible by 2 (since it is odd).
- The sum of the digits (5 + 9) equals 14, which is not divisible by 3, so 59 is not divisible by 3.
- It does not end in 0 or 5, so it's not divisible by 5.
- Checking divisibility by 7: \(59 \div 7 \approx 8.4285\) which is not a whole number.
- Thus, 59 is not divisible by any number other than 1 and 59.
- Therefore, 59 is a prime number.
3. Number 70:
- 70 is an even number (divisible by 2).
- It can also be divided by 5 (since it ends in 0).
- Therefore, 70 is not a prime number.
4. Number 96:
- 96 is also an even number (divisible by 2).
- It can be divided by multiple numbers such as 3, 4, 6, 8, and 12.
- Therefore, 96 is not a prime number.
After evaluating the given numbers, we find that the only prime number among them is:
B. 59.
