46. If a number is divisible by 45, which of the following are prime numbers? (a) 117 (b) 181 (c) 179 (d) 182 47. Express the following as the sum of two odd primes: (a) 44 (b) 36 (c) 24 (d) 18 48. Given odd prime numbers are: 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43. Choose: 44 = 3 + 41 = sum of two odd primes Find the smallest number having four different prime factors. 49. Give an example of a number: (a) which is divisible by 5 but not by 10. (b) which is divisible by 7 but not by 14. (c) which is divisible by both 2 and 6 but not by 16. (d) which is divisible by both 5 and 6 but not by 18.

Let's tackle each part of the question step by step:

Prime Numbers in Given Options: A number is divisible by 45 if it is divisible by both 5 and 9. Here, the task is to identify which of these options are prime numbers:

(a) 117: Not prime, as it can be divided by 3.
(b) 181: Prime, as it has no divisors other than 1 and itself.
(c) 179: Prime, the only divisors are 1 and 179.
(d) 182: Not prime, divisible by 2.
Prime numbers in the list are: (b) 181 and (c) 179.

Expressing Numbers as the Sum of Two Odd Primes:

(a) 44:

Option 1: 44 = 3 + 41 (Both are odd primes)

(b) 36:

Example: 36 = 5 + 31 (Both are odd primes)

(c) 24:

Example: 24 = 11 + 13 (Both are odd primes)

(d) 184:

Example: 184 = 3 + 181 (Both are odd primes)


Smallest Number with Four Different Prime Factors:


To find the smallest number with four different prime factors, multiply the smallest four primes: 2 × 3 × 5 × 7 = 210 .


Examples of Numbers with Specific Divisibility Conditions:

(a) Divisible by 5 but not by 10:

Example: 25 (It is divisible by 5 but not by 10)

(b) Divisible by 7 but not by 14:

Example: 21 (It is divisible by 7 but not by 14)

(c) Divisible by both 2 and 6 but not by 16:

Example: 12 (It is divisible by 2 and 6 but not by 16)

(d) Divisible by both 5 and 6 but not by 18:

Example: 30 (It is divisible by 5 and 6 but not by 18)

Answered by OliviaLunaGracy | 2025-07-21