 # Factors of 986: Prime Factorization, Methods, and Examples

The factors of 986 are numbers that, when divided by 986, give zero as the remainder. This means the numbers that ultimately divide the given number are named as their factors. The provided number’s factors can be positive or negative. Let us know more about factors of 986 in this article.

### Factors of 986

Here are the factors of number 986.

Factors of 986: 1, 2, 17, 29, 34, 58, 493, and 986.

### Negative Factors of 986

The negative factors of 986 are similar to their positive aspects, just with a negative sign.

Negative Factors of 986: –1, -2, -17, -29, -34, -58, -493, and -986

### Prime Factorization of 986

The prime factorization of 986 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 17 x 29

In this article, we will learn about the factors of 986 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 986?

The factors of 986 are 1, 2, 17, 29, 34, 58, 493, and 986. These numbers are the factors as they do not leave any remainder when divided by 986.

The factors of 986 are classified as prime numbers and composite numbers. The prime factors of the number 986 can be determined using the prime factorization technique.

## How To Find the Factors of 986?

You can find the factors of 986 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 986, create a list containing the numbers exactly divisible by 986 with zero remainders. One important thing to note is that 1 and 986 are the 986’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 986 are determined as follows:

$\dfrac{986}{1} = 986$

$\dfrac{986}{2} = 493$

$\dfrac{986}{17} = 58$

$\dfrac{986}{29} = 34$

Therefore, 1, 2, 17, 29, 34, 58, 493, and 986 are the factors of 986.

### Total Number of Factors of 986

For 986, there are eight positive factors and eight negative ones. So in total, there are 16 factors of 986.

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

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the 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 986 is given as follows:

Factorization of 986 is 1 x 2 x 17 x 29.

The exponent of 1, 2, 17, and 29 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 986 is 16. Eight are positive, and eight 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 number factors 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 986 by Prime Factorization  The number 986 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 986 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 986, 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 986 can be expressed as:

986 = 2 x 17 x 29

## Factors of 986 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 986, the factor pairs can be found as:

1 x 986 = 986

2 x 493 = 986

17 x 58 = 986

29 x 34 = 986

The possible factor pairs of 986 are given as (1, 986), (2, 493), (17, 58), and (29, 34).

All these numbers in pairs, when multiplied, give 986 as the product.

The negative factor pairs of 986 are given as:

1 x -986 = 986

-2 x -493 = 986

-17 x -58 = 986

-29 x -34 = 986

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, -2, -17, -29, -34, -58, -493, and -986 are called negative factors of 986.

The list of all the factors of 986, including positive as well as negative numbers, is given below.

Factor list of 986: 1, -1, 2, -2, 17, -17, 29, -29, 34, -34, 58, -58, 493, -493, 986, and -986

## Factors of 986 Solved Examples

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

### Example 1

How many factors of 986 are there?

### Solution

The total number of Factors of 986 is 16.

Factors of 986 are 1, 2, 17, 29, 34, 58, 493, and 986.

### Example 2

Find the factors of 986 using prime factorization.

### Solution

The prime factorization of 986 is given as:

986 $\div$ 2 = 493

493 $\div$ 17 = 29

29 $\div$ 29 = 1

So the prime factorization of 986 can be written as:

2 x 17 x 29 = 986