# DIFFERENCE BETWEEN DIVISORS AND FACTORS

## About "Difference between divisors and factors"

Difference between divisors and factors :

It is the question having had by many students who study math in primary level. Some students consider that both divisors and divisors are same. Actually it is not. There is a difference between them.

Let us look at the difference between them in the next section.

## What is the 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 prime numbers

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 composite numbers

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".

## Some important points about divisors and factors

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.

After having gone through the stuff given above, we hope that the students would have understood "Difference between divisors and factors".

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