Write 'P' for prime and 'C' for composite numbers.

(a) 42
(b) 81
(c) 34
(e) 61
(f) 39
(g) 99
(i) 21
(j) 105
(k) 181

To determine whether a number is prime or composite, let's first understand the definitions:

Prime Numbers : A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Composite Numbers : A composite number is a natural number greater than 1 that has more than two positive divisors.

Let's analyze each number:
(a) 42 : It is composite. 42 can be divided by 1, 2, 3, 6, 7, 14, 21, and 42.
(b) 81 : It is composite. 81 can be divided by 1, 3, 9, 27, and 81.
(c) 34 : It is composite. 34 can be divided by 1, 2, 17, and 34.
(e) 61 : It is prime. 61 can only be divided by 1 and 61.
(f) 39 : It is composite. 39 can be divided by 1, 3, 13, and 39.
(g) 99 : It is composite. 99 can be divided by 1, 3, 9, 11, 33, and 99.
(i) 21 : It is composite. 21 can be divided by 1, 3, 7, and 21.
(j) 105 : It is composite. 105 can be divided by 1, 3, 5, 7, 15, 21, 35, and 105.
(k) 181 : It is prime. 181 can only be divided by 1 and 181.
Thus, the classification is as follows:

(a) 42: C
(b) 81: C
(c) 34: C
(e) 61: P
(f) 39: C
(g) 99: C
(i) 21: C
(j) 105: C
(k) 181: P

Answered by LiamAlexanderSmith | 2025-07-22

The numbers have been classified as follows: 42, 81, 34, 39, 99, 21, and 105 are composite, while 61 and 181 are prime. A prime number has exactly two positive divisors, while a composite number has more than two. Thus, the classifications indicate their divisibility properties.
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Answered by LiamAlexanderSmith | 2025-07-23