Question

(1) Write two numbers which have odd number of factors.

(2) Alex has 39 snacks and 65 sweets and wants to distribute them equally among his friends. What is the minimum number of friends to whom he can distribute them?

[5 marks]

Answer 1

Answer: 1) 4, 9 2) 5

Explanation:
(1) All numbers have even number of factors except the numbers which are perfect squares. For example 4, 9, 16, 25, etc. [1 mark]

Factors of 4 = 1, 2, and 4
Factors of 9 = 1, 3, and 9
Factors of 16 = 1, 2, 4, 8, and 16

Hence, the two numbers with odd number of factors can be 4 and 9. [1 mark]



(2) Number of snacks = 39
Number of sweets = 65

In order to get the minimum number of friends, he has to give maximum possible number of sweets or snacks to each one. i.e. HCF (39, 65)

Factors of 39 = 1, 3, 13, 39
Factors of 65 = 1, 5, 13, 65. [1 mark]

HCF of 39 and 65 = 13 [1 mark]

Thus, the maximum number of sweets or snacks will be 13.
Number of friends who gets 13 snacks = 39 $÷$ 13 = 3
Number of friends who gets 13 snacks = 65 $÷$ 13 = 5
Therefore, the minimum number of friends = 3 + 5 = 8
[1 mark]