1.1 Introduction to whole numbers

Counting numbers: 1,2,3,…

Whole numbers: 0,1,2,3,…

Number system is organized in periods of 3’s

• Ones, thousands, millions, billions, trillions,…

All have three place values

• Ones, tens, hundreds

Divisibility Test

A number is divisible by…

• 2 if the last digit is even

• 3 if the sum of all the digits is divisible by 3

• 4 if the last 2 digits are divisible by 4

• 5 if the last digit is a 5 or 0

• 6 if it is divisible by 2 and 3

• 8 if it is divisible by 2 or 4

• 9 if the sum of all the digits is divisible by 9

• 10 if it ends in 0

Factors

Since 8 × 9 = 72, 8 and 9 are both factors of 72

Prime number

• A counting number greater than 1, whose only factor is 1 and itself

Composite number

• Counting number with factors other than 1 and itself

Prime factorization

• The product of prime numbers that equals the number. The prime numbers are called the prime factors.

Step 1: find 2 factors whose product is the given number.

• 48 = 2 × 24

Step 2: if a factor is prime circle it.

Step 3: if a factor is not prime, find 2 factors whose product is that number.

• 24 = 4 × 6

Step 4: continue and write the given number (composite number) as the product of all the circled primes.

• 4 = 2 × 2

• 48 = 2 × 2 × 2 × 2 × 3

Least and most common multiples of 2 numbers

• Smallest multiple for both numbers

Can use 2 techniques to do this

First technique: list all the multiples of each number

• 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, …

• 18: 18, 36, 54, 72, 90, 108, …

• Common multiples: 36, 72, 108

• Least common multiple: 36

Second technique uses prime factors

• 18 = 3 × 6 12 = 3 × 4

• 6 = 2 × 3 4 = 2 × 2

• 18 = 2 × 3 × 3 12 = 2 × 2 × 3

• LCM = 2 × 2 × 3 × 3

• LCM = 36