Week 2 - Number systems

Question 1

Hindu Arabic numeration system

(types of numbers)

Answer 1

1, 2, 3, 4 = Natural Numbers

0, 1, 2, 3 = Whole numbers

-3, -2, -1, 0, 1, 2, 3 = Integers

1/2 = 0.5, 1/3 = 0.3333 etc. = Rational numbers

Pi, (square root of 2 divided by 1) - Irrational numbers

Question 2

Prime numbers

Answer 2

Prime numbers are only divisible by the number itself and the number 1

They must only have two different divisors (factors)

2, 3, 5, 7, 11, 13

Question 3

Composite numbers

Answer 3

Composite numbers have more than two divisors (factors)

The natural numbers (except 1) that are not prime numbers are composite)

4, 6, 8, 9, 10

1 is neither prime or composite

Question 4

Highest Prime Number

Answer 4

282, 589, 933 - 1
More than 24000 digits

Question 5

Factors and Multiples

Answer 5

Numbers or algebraic expressions are factors (or divisors) of another number if they multiply to give that number.

Factors of 10 are: 1, 2, 5, 10 (come before the number)

A multiple of a whole number is the product of that number and an integer.

Multiples of 10 are: 10, 20, 30, 40, 50 (come after the number)

Question 6

Highest Common Factor HCF

Answer 6

The highest or greatest common factor that will
divide two or more other numbers exactly.

E.g.
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The common factors are: 1, 2, 3, 6
HCF = 6

Question 7

Lowest Common Multiple LCM

Answer 7

The smallest number that is the multiple of
two or more other numbers.

E.g.
Multiples of 5: 5, 10, 15, 20, 25 (etc)
Multiples of 7: 7, 14, 21, 28, 35 (etc)

Common multiples: 35, 70

LCM = 35

Question 8

Divisibility

Answer 8

A number that can be divided evenly without leaving a remainder.

Question 9

Divisible by 2

Answer 9

2 - When the last digit is 0, 2, 4, 6, 8

Question 10

Divisible by 3

Answer 10

3 - When the sum of digits is divisible by 3.

E.g. Is 2358 divisible by 3?
2 + 3 + 5 + 8 = 18.
18 is divisible by 3, therefore 2358 is divisible by 3

Question 11

Divisible by 4

Answer 11

4 - When the last 2 digits are divisible by 4

E.g. 1324 = 1000 + 300 + 24
= 4 x 250 + 4 x 25 x 3 + 24

Question 12

Divisible by 5

Answer 12

Last digit must end in a 5 or 0

Question 13

Divisible by 6

Answer 13

As 6= 2 x 3, the rules for 2 and 3 must both hold.

E.g. 72
The digits add up to a multiple of 3, and it is an even number

Question 14

Divisible by 8

Answer 14

Similar to rule 4, but the last 3 digits must be divisible by 8

Question 15

Divisible by 9

Answer 15

Digits must add up to 9

Question 16

Hindu Arabic Number System

Expanded notation examples

Answer 16

E.g. Write the following numbers as powers of 10 in expanded notation

Question 17

Hindu Arabic Number System

Expanded notation examples

Answer 17

E.g. Write the following numbers as powers of 10 in expanded notation

475 = 4 hundreds, 7 tens and 5 ones
= 4 x 100 + 7 x 10 + 5 x 1
= 4 x 10^2 + 7 x 10^1 + 5 x 10^0

Question 18

Rational vs Irrational Numbers

Answer 18

Rational Numbers: Fractions have a logical and reasonable pattern that repeats (e.g. 0.3333)

Irrational Numbers: Digits continue without pattern, like square and cube root numbers (e.g. Pi: 3.14159)

Question 19

How many prime numbers are there?

Answer 19

25

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 20

Triangular numbers (diagram with blue dots in triangles)

Answer 20

Natural numbers which can be drawn as dots and arranged in a triangular shape

1, 3, 6, 10

Question 21

Square numbers (diagram with pink circles in squares)

Answer 21

Natural numbers which can be drawn as dots and arranged in a square shape

E.g. 1, 4, 9, 16

Question 22

Cubic Numbers

Answer 22

A number raised to the third power which is
indicated by a small 3 to its upper-right.

1 is the first cube number because 1 x 1 x 1 = 1

8 is the second cube number, because 2 x 2 x 2 = 8

27 is the third cube number, because 3 x 3 x 3 = 27

64 is the fourth cube number, because 4 x 4 x 4 = 64

Question 23

First 4 cube numbers

Answer 23

1, 8, 27, 64