DIFFERENCE BETWEEN DIVISORS AND FACTORS

The divisors of a number other than 1 and the number itself are called the factors of that number. 

Let us consider the table given below. 

In the above table, let us consider the number 42.

Divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Here, other than 1 and 42, the remaining divisors are called factors.  

More clearly, 

2, 3, 6, 7, 14 and 21 are called as factors. 

From the above explanation, we can know the following important fact. 

That is, all the factors are divisors and all the divisors are not factors. 

In the above example, 1 and 42 are divisors, but they are not factors. 

Factors of a Prime Number

Let us consider the prime number 7. 

The divisors of 7 are 1 and 7. 

According to the stuff explained on "Divisors and factors", 7 has no factor. 

So, prime number has no factors and it will have only two divisors. They are 1 and the number itself. 

Factors of a Composite Number

If a number is not prime, then it is composite.

If a number has more than two divisors, then it has factor or factors and it is composite. 

For example, the number 4 has the divisors 1, 2 and 4.

Since it has more than two divisors, the number 4 is composite.

According to the stuff explained on "Divisors and factors", 4 has one factor, that is "2". 

Points to Remember

1)  "1" has only one divisor, that is 1. So 1 is neither prime nor composite.  

2)  1 and number itself are divisors of any number. 

3)  Is there any number which has no divisor ? 

No, because 1 is a divisor of all numbers.

4) Some numbers have more than two divisors. Those numbers are called as composite numbers. 

5) Some numbers have exactly two divisors. Those numbers are called as prime numbers. 

6)  Prime numbers has no factors. 

7) All factors are divisors, but all divisors are not factors. 

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.