Factors of 801: Prime Factorization, Methods, and Examples

The factors of a three-digit number 801 are 1,3, 9, 89, 267, and 801 when used these as divisors give us no remainder with dividend 801 and the quotient is also a whole number so we claim that these are factors of 801. 

Factors Of 801

Factors of 801

Here are the factors of number 801.

Factors of 801: 1, 3, 9, 89, 267, and 801

Negative Factors of 801

The negative factors of 801 are similar to its positive aspects, just with a negative sign.

Negative Factors of 801: -1, -3, -9, -89, -267, and -801

Prime Factorization of 801

The prime factorization of 801 is the way of expressing its prime factors in the product form.

Prime factorization of eight hundred and one

Prime Factorization: 3 x 3 x 89

In this article, we will learn about the factors of 801 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 801?

The factors of 801 are 1, 3, 9, 89, 267, and 801. These numbers are the factors as they do not leave any remainder when divided by 801.

The factors of 801 are classified as prime numbers and composite numbers. The prime factors of the number 801 can be determined using the prime factorization technique.

How To Find the Factors of 801?

You can find the factors of 801 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 801, create a list containing the numbers that are exactly divisible by 801 with zero remainders. One important thing to note is that 1 and 801 are the 801’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 801 are determined as follows:

\[\dfrac{801}{1} = 801\]

\[\dfrac{801}{3} = 267\]

\[\dfrac{801}{9} = 89\]

\[\dfrac{801}{89} = 9\]

\[\dfrac{801}{267} = 3\]

\[\dfrac{801}{801} = 1\]

Therefore, 1, 3, 9, 89, 267, and 801 are the factors of 801.

Total Number of Factors of 801

For 801, there are six positive factors and six negative ones. So in total, there are twelve factors of 801. 

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 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 801 is given as:

Factorization of 801 is 3 x 3 x 89.

The exponent of 3 and 89 is 2,1.

Adding 1 to each and multiplying them together results in 6.

Therefore, the total number of factors of 801 is twelve. Six are positive, and six 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 801 by Prime Factorization

The number 801 is a composite. 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 801 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 801, 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 801 can be expressed as:

801 = 3 x 3 x 89

Factors of 801 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.

Pairs of eight hundred and one

For 801, the factor pairs can be found as:

1 x 801 = 801

3 x 267 = 801

9 x 89 = 801

The possible factor pairs of 801 are given as (1, 801), (3, 267), and (9, 89).

All these numbers in pairs, when multiplied, give 801 as the product.

The negative factor pairs of 801 are given as:

-1 x -801 = 801

-3 x -267 = 801

-9 x -89 = 801

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, -89, -267, and -801 are called negative factors of 801.

The list of all the factors of 801, including positive as well as negative numbers, is given below.

Factor list of 801: 1, -1, 3, -3, 9, -9, 89, -89, 267, -267, 801 and -801

Factors of 801 Solved Examples

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

Example 1

How many factors of 801 are there?


The total number of Factors of 801 is m.

Factors of 801 are 1, 3, 9, 89, 267, and 801

Example 2

Find the factors of 801 using prime factorization.


The prime factorization of 801 is given as:

801 $\div$ 3 = 267 

267 $\div$ 3 = 89 

89 $\div$ 89 = 1 

So the prime factorization of 801 can be written as:

3 x 3 x 89 = 801

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