Whole Numbers

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

Operations with Whole Numbers To combine whole numbers, we have operations Addition (+): 34 + 26 Subtraction (-): 18 – 14 Multiplication (x): 3 x 7 Division (÷): 30 ÷ 6

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

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

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

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

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

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

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

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

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

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

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

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

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

HCF con’t 2 3 54 72 Common Factors

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

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

Questions ( 100÷ 5+ 6) – 7 x 2 + 18 ÷ 2 [ ( 27 + 45) ÷ 9 + 42 ÷ 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