Let's determine which of the given numbers is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
We'll examine each option step-by-step:
1. 72
- 72 is an even number (it ends in 2).
- By definition, any even number greater than 2 is not a prime number because it can be divided by 2.
- Therefore, 72 is not a prime number.
2. 141
- 141 is an odd number.
- To check if it's prime, we need to see if it has any divisors other than 1 and 141.
- 141 can be divided by 3 (since the sum of its digits, 1 + 4 + 1 = 6, is divisible by 3).
- Since 141 is divisible by 3 (141 ÷ 3 = 47), it is not a prime number.
3. 107
- 107 is an odd number.
- We need to check if 107 is divisible by any prime number less than its square root (approximately 10.34).
- Check divisibility by 2, 3, 5, and 7 (prime numbers less than 11):
- 107 is not even, so it’s not divisible by 2.
- The sum of the digits (1 + 0 + 7 = 8) is not divisible by 3.
- 107 does not end in 0 or 5, so it’s not divisible by 5.
- 107 divided by 7 is approximately 15.285, not an integer.
- As 107 is not divisible by any of these primes, it has no divisors other than 1 and 107 itself.
- Therefore, 107 is a prime number.
4. 196
- 196 is an even number (it ends in 6).
- By definition, any even number greater than 2 is not a prime number because it can be divided by 2.
- Therefore, 196 is not a prime number.
From the analysis, the number 107 is the only number that is a prime. Therefore, the correct answer is:
C. 107
