Explore a vast range of topics and get informed answers at IDNLearn.com. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
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
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
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.