Factors and Multiples

Factors

A factor of a number is defined as the number that divides the given number exactly without any remainder.

Examples:

We know that 8 is divisible by 4 completely without any remainder. Therefore, 4 is the factor of 8.

Alternatively, the factor of a number is defined as two numbers such that the product of numbers is equal to the given number.

Examples:

The product of the numbers 3 and 2 is equal to 6. Therefore, 2 and 3 are the factors of 6.

A number may have many factors.

Properties of Factors

• A number may have many factors.
• Every number is a factor of itself.
• 1 is the factor of every number.
• Every number other than 1 has at least two factors, i.e., 1 and itself.

Multiples

The multiples of the number are the product of the numbers with the natural numbers.

Examples:

The first ten multiples of the number 12 are:

12 × 6 = 72

12 × 7 = 84

12 × 8 = 96

12 × 9 = 108

12 × 10 = 120

12 × 1 = 12

12 × 2 = 24

12 × 3 = 36

12 × 4 = 48

12 × 5 = 60

Properties of Multiples

• Every number is a multiple of itself.
• 1 × 8 = 8; 1 × 14 = 14
• Every number is the multiple of 1.
• 8 × 1 = 8; 14 × 1 = 14
• The first multiple of the number is equal to the number.
• The first multiple of 8 is 1 × 8 = 8
• Every multiple of the number is either equal to the number or greater than the number.
• The multiple of 3 are 3, 6, 9, 12, 15, ……
• The multiples of an even number are always even.
• The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, …..
• The multiples of an odd number are alternatively odd and even.
• The multiples of 9 are 9, 18, 27, 36, 45, 54, ……
• A number can have an infinite number of multiples.