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Answer :
To identify the prime numbers from the given options, let’s first understand what a prime number is. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly (without a remainder) by 1 and the number itself.
Now, let’s check each of the options:
A. 21 - This number is not prime because it can be divided evenly by 1, 3, 7, and 21.
B. 33 - This number is not prime because it can be divided evenly by 1, 3, 11, and 33.
C. 37 - This number is a prime number because the only divisors are 1 and 37.
D. 63 - This number is not prime because it can be divided evenly by 1, 3, 7, 9, 21, and 63.
E. 77 - This number is not prime because it can be divided evenly by 1, 7, 11, and 77.
F. 89 - This number is a prime number because the only divisors are 1 and 89.
Based on this analysis:
- 37 is a prime number.
- 89 is a prime number.
Therefore, the correct choice for the prime numbers is C. 37 and F. 89.
Now, let’s check each of the options:
A. 21 - This number is not prime because it can be divided evenly by 1, 3, 7, and 21.
B. 33 - This number is not prime because it can be divided evenly by 1, 3, 11, and 33.
C. 37 - This number is a prime number because the only divisors are 1 and 37.
D. 63 - This number is not prime because it can be divided evenly by 1, 3, 7, 9, 21, and 63.
E. 77 - This number is not prime because it can be divided evenly by 1, 7, 11, and 77.
F. 89 - This number is a prime number because the only divisors are 1 and 89.
Based on this analysis:
- 37 is a prime number.
- 89 is a prime number.
Therefore, the correct choice for the prime numbers is C. 37 and F. 89.
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