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 Ă— 6 = 72
12 Ă— 7 = 84
12 Ă— 8 = 96
12 Ă— 9 = 108
12 Ă— 10 = 120
12 Ă— 1 = 12
12 Ă— 2 = 24
12 Ă— 3 = 36
12 Ă— 4 = 48
12 Ă— 5 = 60
Properties of Multiples
- Every number is a multiple of itself.
- 1 Ă— 8 = 8; 1 Ă— 14 = 14
- Every number is the multiple of 1.
- 8 Ă— 1 = 8; 14 Ă— 1 = 14
- The first multiple of the number is equal to the number.
- The first multiple of 8 is 1 Ă— 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.