# Module 1 - Unit 6: Number Theory

## Self-Audit

For the multiple choice questions below, choose one answer, (a), (b), (c) or (d), that is CORRECT by clicking the appropriate box.
Calculators are NOT allowed unless it is indicated in the question.

## Section 6.1 - Factors and Prime Numbers

Question 1
 How many factors does 28 have? (A) 2   (B) 4 (C) 6 (D) 8
Question 2
 How many prime factors does 28 have? (A) 1   (B) 2 (C) 3 (D) 4
Question 3
 Which of these numbers is a prime number? (A) 39   (B) 63 (C) 78 (D) 97
Question 4
 What is the smallest number that has prime factors 2, 3 and 5? (A) 6   (B) 15 (C) 30 (D) 60

## Section 6.2 - Prime Factors

Question 5
 How many prime factors does the number 24 have? (A) 1   (B) 2 (C) 3 (D) 4
Question 6
 How many prime factors does a prime number have? (A) 0   (B) 1 (C) 2 (D) None of these
Question 7
 What is the smallest number that has 3 different prime factors? (A) 6   (B) 24 (C) 30 (D) 60
Question 8
 The prime factors of a number are 2, 5 and 7. What is the second smallest number that has these prime factors? (A) 35   (B) 70 (C) 140 (D) None of these

## Section 6.3 - Index Notation

Question 9
 What is the value of 34? (A) 9   (B) 12 (C) 27 (D) 81
Question 10
 What is the missing number x in the equation below? 64 = 2x (A) 2   (B) 4 (C) 6 (D) 8
Question 11
 What is 53 × 22? (A) 50   (B) 60 (C) 100 (D) 500
Question 12
 What is the value of x in the equation below? 34 × 35 = 3x (A) 9   (B) 12 (C) 20 (D) None of these

## Section 6.4 - Highest Common Factor and Lowest Common Multiple

Question 13
 What is the highest common factor of 48 and 60? (A) 6   (B) 8 (C) 12 (D) 24
Question 14
 What is the highest common factor of 20, 30 and 45? (A) 5   (B) 10 (C) 15 (D) None of these
Question 15
 What is the lowest common multiple of 5 and 9? (A) 15   (B) 27 (C) 45 (D) 90
Question 16
 What is the lowest common multiple of 4, 7 and 10? (A) 40   (B) 70 (C) 140 (D) 280

## Section 6.5 - Squares and Square Roots

Question 17
 What is the square of 20? (A) 40   (B) 200 (C) 400 (D) None of these
Question 18
 What is the value of √ ? 81
(A)3   (B)7
(C)9
(D)27
Question 19
 What is the value of √ ? 324
(A)18   (B)36
(C)108
(D)None of these
Question 20
 The area of a square is 196 cm2 . What is the side length of this square? (A) 7 cm   (B) 14 cm (C) 28 cm (D) 49 cm

## Section 6.6 - Sets and Venn Diagrams

The whole numbers 1 to 15 are shown in the Venn diagram below. Question 21
 Set A is described by: (A) Odd numbers   (B) Even numbers (C) Multiples of 4 (D) Whole numbers
Question 22
 Set B is described by: (A) Odd Numbers   (B) Even numbers (C) Multiples of 4 (D) Whole numbers
Question 23
 The complement of A is described by: (A) Odd numbers   (B) Even numbers (C) Multiples of 4 (D) Whole numbers
Question 24
 The union of A and B is described by: (A) Odd numbers   (B) Even numbers (C) Multiples of 4 (D) Whole numbers

## Section 6.7 - Solving Logic Problems with Venn Diagrams

There are 45 students in a school canteen.
18 of them have finished eating.
The others are eating burgers or fries or both burgers and fries.
A total of 24 students are eating fries and 17 are eating burgers.

Question 25
 How many students are eating burgers and fries? (A) 3   (B) 10 (C) 14 (D) 27
Question 26
 How many students are eating burgers without fries? (A) 3   (B) 10 (C) 14 (D) 27
Question 27
 How many students are eating only fries? (A) 3   (B) 10 (C) 14 (D) 27
Question 28
 In a class of 38 students, 22 say they like pancakes and 16 say they like maple syrup. 6 of the students do not like either. How many of the students like both pancakes and maple syrup? (A) 6   (B) 8 (C) 10 (D) 16 Mark your answers.