 # Factors of 981: Prime Factorization, Methods, and Examples

The factors of 981 are the numbers that give a zero remainder when 981 acts as the dividend for such numbers. The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

### Factors of 981

Here are the factors of number 981.

Factors of 981: 1, 3, 9, 109, 327, 981

### Negative Factors of 981

The negative factors of 981 are similar to its positive aspects, just with a negative sign.

Negative Factors of 981: -1, -3, -9, -109, -327, and -981

### Prime Factorization of 981

The prime factorization of 981 is the way of expressing its prime factors in the product form.

Prime Factorization: $3^{2}$ x 109

In this article, we will learn about the factors of 981 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 981?

The factors of 981 are 1, 3, 9, 109, 327, and 981. These numbers are the factors as they do not leave any remainder when divided by 981.

The factors of 981 are classified as prime numbers and composite numbers. The prime factors of the number 981 can be determined using the prime factorization technique.

## How To Find the Factors of 981?

You can find the factors of 981 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 981, create a list containing the numbers that are exactly divisible by 981 with zero remainders. One important thing to note is that 1 and 981 are the 981’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 981 are determined as follows:

$\dfrac{981}{1} = 981$

$\dfrac{981}{3} = 327$

$\dfrac{981}{9} = 109$

$\dfrac{981}{981} = 1$

Therefore, 1, 3, 9, 109, 327, and 981 are the factors of 981.

### Total Number of Factors of 981

For 981, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 981.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 981 is given as:

Factorization of 981 is 1 x $3^{2}$ x 109.

The exponent of 1 and 109 is 1 and that of 3 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 981 is 12. 6 are positive, and 6 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 981 by Prime Factorization  The number 981 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 981 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 981, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 981 can be expressed as:

981 = $3^{2}$ x 109

## Factors of 981 in Pairs  The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 981, the factor pairs can be found as:

1 x 981 = 981

3 x 327 = 981

9 x 109 = 981

The possible factor pairs of 981 are given as (1, 981), (3, 327), and (9, 109).

All these numbers in pairs, when multiplied, give 981 as the product.

The negative factor pairs of 981 are given as:

-1 x -981 = 981

-3 x -327 = 981

-9 x -109 = 981

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -9, -109, -327, and -981 are called negative factors of 981.

The list of all the factors of 981, including positive as well as negative numbers, is given below:

Factor list of 981: 1, -1, 3, -3, 9, -9, 109, -109, 327, -327, 981, and -981

## Factors of 981 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 981 are there?

### Solution

The total number of Factors of 981 is 6.

Factors of 981 are 1, 3, 9, 109, 327, and 981.

### Example 2

Find the factors of 981 using prime factorization.

### Solution

The prime factorization of 981 is given as:

981 $\div$ 3 = 327

327 $\div$ 3 = 109

109 $\div$ 109 = 1

So the prime factorization of 981 can be written as:

$3^{2}$ x 109 = 981