1. Whole Numbers

2. Whole Numbers Whole numbers: Numbers 0,1,2,3,4,5 and so on
Natural Numbers: Counting numbers, whole numbers but without zero, or positive whole numbers

3. Operations with Whole Numbers
To combine whole numbers, we have operations
Addition (+):
Subtraction (-): 18 – 14
Multiplication (x): 3 x 7
Division (÷): 30 ÷ 6

4. Order of Operations BEDMAS
Brackets, Exponents, Multiplication/Division, Addition/Subtraction
Operations on the same level (x/÷, +/-) work from left to right
Within brackets, do innermost brackets first

5. Questions 32÷4+9 234 ÷ (10+3) – 9 2 + 14 - 3 + 5 + 7 - 25 x 0
[6-4 x (3 x {4-4})] + 1
Ans: 17, 9, 25, 0, 7

6. Divisibility
A number is divisible by another number if when you divide them, there is no remainder
14 is divisible by 7 because it is 2 with no remainder

7. Divisibility Rules 2: one’s digit is even
3: sum of digits is divisible by 3
4: last 2 digits are divisible by 4
5: number ends in 0 or 5
6: divisible by both 2 and 3
9: sum of digits is divisible by 9
10: number ends in 0
Yes, no

8. Factors and Multiples
Prime numbers: a natural number that exactly have 2 factors
3, 5, 19
Factor: if a number is divisible by the number, then it is a factor of that number
7 is a factor of 21
Multiple: the product of the number and some other whole number
Multiples of 3: 3, 6, 9, 12, 15…
Composite number: a natural number that has 3 or more factors
24, 15, 100

9. Prime Factorization Factor Tree: 60 Prime factorization of 60: 2x2x3x5
In exponential form or index notation:
22x3x5

10. Prime Factorization con’t
Repeated division 60
÷ 2 30 15
÷ 5 3
÷ 3 1
Prime Factors

11. Finding Factors Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 1 x 24 = 24

12. Finding Factors con’t Using Prime Factors: 120 = 23 x 31 x 51 x 50 3021 2 6 22 4 12 23 8 24
x 51 30 31 20 5 15 21 10 22 60 23 40
120

13. Counting Factors Rainbow method:
Factors of 24: there are 8 factors of 24

14. Counting Factors con’t
24 = 23 x 31
2 options x 30 31 20 1 3 21 2 6 22 4 12 23 8 24
Take the exponent numbers and add 1. Then, multiply them all together.
(3+1) x (1+1) = 8 factors
4 options

15. Highest Common Factor 72, 54 72 = 2x3x3 x2x2 54 = 2x3x3
HCF(54,72) = 2x3x3 = 18
Find all common prime factors, and multiply together.

16. HCF con’t ÷ 72 54 2 36 27 3 12 9 4
2x3x3 = 18

17. HCF con’t 2 3 54 72
Common Factors

18. Least Common Multiple Multiples of 12: 12, 24, 36, 48, 60, 72…
Common Multiples of 12 and 18 are 36, 72
Least common multiple is 36

19. LCM con’t 12 = 2 x 3 x 2 18 = 2 x 3 x 3 HCF(12,18) = 6
LCM = HCF x (product of remaining prime factors)
6 x (2 x 3) = 36
LCM(12,18)= 36

20. Questions
( 100÷ 5+ 6) – 7 x ÷ 2
[ ( ) ÷ ÷ 6 ] x 3
Find the LCM and HCF of 45, 18
Prime factorize 1000
How many factors does 96 have?
Which of the following is divisible by 6?
45, 23, 36, 27, 96, 78
19, 45, hcf = 9, lcm = 90, 2^3x5^3, 12, no, no, yes, no, no, yes