# 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.

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?

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

2. Is 4 a factor of 1121?

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

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