Page 35 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 15

1.2 Factors and Multiples

Factors of a number are whole numbers that can divide the number evenly (i.e. with no remainder).
1 is a factor of every For example, to find factors of 12, divide the number 12 by 1, 2, 3, 4,...; the numbers that divide 12
number and every
number is a factor evenly are its factors.
of itself. 12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1

A number is divisible Therefore, 1, 2, 3, 4, 6, and 12 are factors of 12.
by another number if it
divides evenly with no Note: 5, 7, 8, 9, 10, and 11 do not divide 12 evenly. Therefore, they are not factors of 12.
remainder.
We can also express factors of a number by showing how the product of two factors results in the number.

12 = 1 × 12 or 12 × 1 1 2 3 4 6 12
12 = 2 × 6 or 6 × 2
12 = 3 × 4 or 4 × 3
Multiples of a number are the products of the number and the natural numbers (1, 2, 3, 4,...). For
example,

10 × 1 = 10 10 × 2 = 20 10 × 3 = 30 10 × 4 = 40 10 × 5 = 50

Therefore, multiples of 10 are 10, 20, 30, 40, 50, etc.

Note: Multiples of a number can be divided by the number with no remainder.

Useful Divisibility Rules

■ A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
■ A number is divisible by 3 if the sum of its digits is divisible by 3.
■ A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
■ A number is divisible by 5 if it ends in 0 or 5.
■ A number is divisible by 6 if it is divisible by 2 and 3.
■ A number is divisible by 9 if the sum of its digits is divisible by 9.
■ A number is divisible by 10 if it ends in 0.

Prime Numbers and Composite Numbers

A prime number is a natural number (counting number) greater than 1 whose only factors are 1
All even numbers are and the number itself.
composite numbers,
except for 2, which is a For example, 7 is a prime number because it only has two factors: 1 and 7.
prime number.
A composite number is a natural number that has at least one factor other than 1 and the number
itself; i.e. all natural numbers that are not prime numbers are composite numbers.
For example, 8 is a composite number because it has more than two factors: 1, 2, 4, and 8.
Note: 0 and 1 are neither prime numbers nor composite numbers.