Properties of Factors

The properties of factors are discussed step by step according to its property.

Property (1):

Every whole number is the product of 1 and itself so

(i) Each number is a factor of itself. 

19 x 1 = 19, 

So, 19 is the factor of 19. 

(ii) 1 is the factor of every number. 

We know that a number multiplied by 1 is the number itself. So, 1 is a factor of every number.

For example

21 ÷ 1 = 21. So, 1 is the factor of 21,

96 ÷ 1 = 96, So, 1 is a factor of 96.

31 x 1 = 31, So, 1 is the factor of 31.

Property (2):

Every number is a factor of zero (0)

As, 7 x 0 = 0,

17 x 0 = 0,

93 x 0 = 0

So, 7, 17, 93, ……, etc., are the factors of 0.

Property (3):

1 is the smallest factor of every number. 

1 is the smallest factor of a multiple and the greatest factor of a multiple is the multiple itself.

A number is a factor of itself. SO, a number itself is its own greatest factor. For example 73 ÷ 1 = 73 so, 73 and 1 are the factors. 73 is the greatest factors.

Property (4):

Every number other than 1 has at least two factors, namely the number itself and 1.

We know that 1 and the number itself are always the factors of every number. This means that every number has at least 2 factors.

Therefore, the properties of factors are explained above so, that student can understand each property.

Properties of Factors

Property 1: A number has a finite number of factors.

Property 2: 1 and the number itself are the factors of every number.

Property 3: 1 is the smallest factor of any number.

Property 4: The number itself is the greatest factor of every number.

Property 5: Factors of a number are always smaller or equal to the number.

Property 6: Every factor of a number is the exact divisor of the number.

Properties of Factors

To find that whether a number is a factor of another number, we divide the bigger number by the smaller number. If the remainder is zero, we say that the divisor is a factor of the dividend.

For example:

1. Is 5 a factor of 625?

5 is a Factor of 625

Here, 5 divides 625 exactly. So 5 is a factor of 625.

2. Is 4 a factor of 1121?

4 is Not a Factor of 1121

Here, 4 does not divide 1121 exactly. So 4 is not a factor of 1121.

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Related Concept

Factors and Multiples by using Multiplication Facts

Factors and Multiples by using Division Facts


Properties of Multiples

Examples on Multiples


Factor Tree Method

Properties of Factors

Examples on Factors

Even and Odd Numbers

Even and Odd Numbers Between 1 and 100

Examples on Even and Odd Numbers

4th Grade Math Activities

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