1. Which of the following are even numbers? 16, 27, 21, 35, 28, 59, 280, 559

2. Which of the following numbers are prime? 1, 5, 17, 28, 61, 89, 78, 88, 97, 47, 81

3. List all twin-primes between 1 and 50.

4. List all prime numbers between 51 and 100.

5. Give four examples of pairs of co-primes.

6. Write the prime factorization of each of the following numbers using division by prime numbers:
a. 30
b. 72
c. 84
d. 210
e. 728

7. Write the prime factorisation of each of the following numbers using factor tree:
a. 45
b. 69
c. 96
d. 210
e. 450

8. Which of the following are co-prime numbers?
a. 48, 52
b. 33, 51
c. 9, 16
d. 30, 45

Even Numbers : A number is even if it is divisible by 2. Let's check each number:

16: Even (divisible by 2)
27: Odd (not divisible by 2)
21: Odd (not divisible by 2)
35: Odd (not divisible by 2)
28: Even (divisible by 2)
59: Odd (not divisible by 2)
280: Even (divisible by 2)
5592: Even (divisible by 2)

Therefore, the even numbers are: 16, 28, 280, 5592.

Prime Numbers : A prime number is greater than 1 and has no positive divisors other than 1 and itself. Let's check each number:

1: Not prime
5: Prime
17: Prime
28: Not prime
61: Prime
89: Prime
78: Not prime
88: Not prime
97: Prime
47: Prime
81: Not prime

Therefore, the prime numbers are: 5, 17, 61, 89, 97, 47.

Twin-Primes Between 1 and 50 : Twin primes are pairs of primes that have a difference of 2. Let's list them:

(3, 5)
(5, 7)
(11, 13)
(17, 19)
(29, 31)
(41, 43)

Therefore, the twin-prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43).

Prime Numbers Between 51 and 100 : Let's list them:

53
59
61
67
71
73
79
83
89
97

Therefore, the prime numbers between 51 and 100 are: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Pairs of Co-Primes : Co-primes (or coprime numbers) are numbers that have no common factor other than 1. Some pairs are:

(8, 15)
(14, 25)
(21, 22)
(35, 64)

These pairs have no common divisors other than 1.

Prime Factorization Using Division by Primes :

a. 30 = 2 × 3 × 5
b. 72 = 2 3 × 3 2
c. 84 = 2 2 × 3 × 7
d. 210 = 2 × 3 × 5 × 7
e. 728 = 2 3 × 91 = 2 3 × 7 × 13


Prime Factorization Using Factor Tree :

a. 45: 45 = 3 2 × 5
b. 69: 69 = 3 × 23
c. 96: 96 = 2 5 × 3
d. 210: 210 = 2 × 3 × 5 × 7
e. 450: 450 = 2 × 3 2 × 5 2


Co-prime Numbers :

a. 48, 52: Not co-prime (common factor is 4)
b. 33, 51: Not co-prime (common factor is 3)
c. 9, 16: Co-prime (no common factor other than 1)
d. 30, 45: Not co-prime (common factor is 15)



Thus, among the given pairs, the co-prime pair is (9, 16).

Answered by EmmaGraceJohnson | 2025-07-06