Properties of Numbers: Odd/Even, Prime/Composite, and Divisibility Rules

Odd and Even Numbers

1. Which of the following is an even number?
   • Answer: 24 (Even numbers end in 0, 2, 4, 6, or 8).
2. What is the sum of two odd numbers?
   • Answer: b) Even
     (The sum of two odd numbers is always even, e.g., 3 + 5 = 8).
3. What is the product of two even numbers?
   • Answer: b) Even
     (The product of two even numbers is always even, e.g., 4 × 6 = 24).
4. Is the number 2017 odd or even?
   • Answer: Odd
     (2017 ends in 7, which is odd).
5. Which of the following is an odd number?
   • Answer: 51
     (51 ends in 1, which is odd).
6. If you add an even number and an odd number, what type of number will you get?
   • Answer: a) Odd
     (The sum of an even and an odd number is always odd, e.g., 4 + 5 = 9).
7. Is the number 0 even or odd?
   • Answer: Even
     (0 is divisible by 2, so it is even).
8. What is the product of 2 odd numbers?
   • Answer: a) Odd
     (The product of two odd numbers is always odd, e.g., 3 × 5 = 15).
9. Which of the following is the sum of two even numbers?
   • Answer: b) 20
     (The sum of two even numbers is always even, e.g., 10 + 10 = 20).
10. Which of the following is not an even number?
    • Answer: 9
      (9 is odd, as it ends in 9).

Prime and Composite Numbers

11. Which of the following is a prime number?
    • Answer: 11
      (Prime numbers are divisible only by 1 and themselves, and 11 is prime).
12. What is the smallest prime number?
    • Answer: 2
      (2 is the smallest prime number and the only even prime).
13. Which of the following is not a prime number?
    • Answer: 4
      (4 is divisible by 1, 2, and 4, so it’s composite, not prime).
14. Is the number 1 a prime number? Justify your answer.
    • Answer: No
      (1 is not a prime number because prime numbers must be greater than 1).
15. Which of the following numbers is composite?
    • Answer: 18
      (18 is divisible by 1, 2, 3, 6, 9, and 18, so it is composite).
16. Is the number 31 prime or composite?
    • Answer: Prime
      (31 is only divisible by 1 and itself, so it is prime).
17. How many prime numbers are there between 1 and 20?
    • Answer: 8
      (The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19).
18. What is the prime factorization of 36?
    • Answer: 2 × 2 × 3 × 3
      (36 = $2^2 \times 3^2$22×32).
19. Which of the following is not a composite number?
    • Answer: 23
      (23 is prime, not composite).
20. Which of the following is a composite number?
    • Answer: 32
      (32 is divisible by 1, 2, 4, 8, 16, and 32, so it’s composite).

Divisibility Rules

21. Which number is divisible by 3?
    • Answer: 123
      (Sum of digits: 1 + 2 + 3 = 6, divisible by 3).
22. Which of the following numbers is divisible by 5?
    • Answer: 50
      (Numbers divisible by 5 end in 0 or 5).
23. Is the number 585 divisible by 9?
    • Answer: Yes
      (Sum of digits: 5 + 8 + 5 = 18, divisible by 9).
24. Which of the following is divisible by 4?
    • Answer: 128
      (The last two digits, 28, are divisible by 4).
25. What is the divisibility rule for 6?
    • Answer: c) Divisible by both 2 and 3
      (A number divisible by both 2 and 3 is divisible by 6).

Bonus Questions:

26. What is the smallest even prime number?
    • Answer: 2
      (2 is the smallest even prime number).
27. If a number is divisible by 4 and 6, is it also divisible by 12? Justify your answer.
    • Answer: Yes
      (If a number is divisible by both 4 and 6, it is also divisible by 12, because 12 is the least common multiple of 4 and 6).
28. Which of the following numbers is divisible by both 2 and 3?
    • Answer: 18
      (18 is divisible by both 2 and 3, as 18 ÷ 2 = 9 and 18 ÷ 3 = 6).