Factors of 721: Prime Factorization, Methods, and Examples

The numbers that can split evenly into 721 and leave zero as a remainder on division with 721 are called the factors of 721, as the number of factors of 721 is 4 which is more than 2, hence, it is considered a composite number. 

Factors Of 721

1, 7, 103, and 721 are the factors of 721.

Factors of 721

Here are the factors of number 721.

Factors of 721: 1, 7, 103, and 721.

Negative Factors of 721

The negative factors of 721 are similar to its positive aspects, just with a negative sign.

Negative Factors of 721: -1, -7, -103, and -721.

Prime Factorization of 721

The prime factorization of 721 is the way of expressing its prime factors in the product form.

Prime factorization of seven hundred and twenty one

Prime Factorization: 7 x 103

In this article, we will learn about the factors of 721 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 721?

The factors of 721 are 1, 7, 103, and 721. These numbers are the factors as they do not leave any remainder when divided by 721.

The factors of 721 are classified as prime numbers and composite numbers. The prime factors of the number 721 can be determined using the prime factorization technique.

How To Find the Factors of 721?

You can find the factors of 721 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 721, create a list containing the numbers that are exactly divisible by 721 with zero remainders. One important thing to note is that 1 and 721 are the 721’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 721 are determined as follows:

\[\dfrac{721}{1} = 721\]

\[\dfrac{721}{7} = 103\]

\[\dfrac{721}{103} = 7\]

\[\dfrac{721}{721} = 1\]

Therefore, 1, 7, 103, and 721 are the factors of 721.

Total Number of Factors of 721

For 721, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 721. 

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 721 is given as:

Factorization of 721 is 1 x 7 x 103.

The exponent of 1, 7, and 103 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of721 is 8. 4 are positive, and 4 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 721 by Prime Factorization

The number 721 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 721 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 721, 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 721 can be expressed as:

721 = 7 x 103

Factors of 721 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 seven hundred and twenty one

For 721, the factor pairs can be found as:

1 x 721 = 721

7 x 103 = 721 

The possible factor pairs of 721 are given as (1, 721) and (7, 103 ).

All these numbers in pairs, when multiplied, give 721 as the product.

The negative factor pairs of 721 are given as:

-1 x -721 = 721 

-103 x -7 = 721

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, -7, -103, and -721 are called negative factors of 721.

The list of all the factors of 721, including positive as well as negative numbers, is given below.

Factor list of 721: 1, -1, 7, -7, 103, -103, 721, and -721

Factors of 721 Solved Examples

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

Example 1

How many factors of 721 are there?


The total number of Factors of 721 is 4.

Factors of 721 are 1, 7, 103, and 721.

Example 2

Find the factors of 721 using prime factorization.


The prime factorization of 721 is given as:

721 $\div$ 7 = 103 

103 $\div$ 103 = 1 

So the prime factorization of 721 can be written as:

7 x 103 = 721

Factors of 720|Factors List| Factors of 722