Factors of 709: Prime Factorization, Methods, and Examples

709 is a prime number that cannot be further divided by any number other than 1 and 709 itself. Like all prime numbers, 709 is only a multiple of 1 and itself. This means that it can be divided by only one and itself, without a remainder. 

Factors Of 709

There are infinite prime numbers in the number line a lot of which are not yet discovered.

Factors of 709

Here are the factors of number 709.

Factors of 709: 1 and 709

Negative Factors of 709

The negative factors of 709 are similar to its positive aspects, just with a negative sign.

Negative Factors of 709: -1 and -709

Prime Factorization of 709

The prime factorization of 709 is the way of expressing its prime factors in the product form.

Prime factorization of seven hundred and nine

Prime Factorization: 1 x 709

In this article, we will learn about the factors of 709 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 709?

The factors of 709 are 1 and 709. These numbers are the factors as they do not leave any remainder when divided by 709.

The factors of 709 are classified as prime numbers and composite numbers. The prime factors of the number 709 can be determined using the prime factorization technique.

How To Find the Factors of 709?

You can find the factors of 709 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 709, create a list containing the numbers that are exactly divisible by 709 with zero remainders. One important thing to note is that 1 and 709 are the 709’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 709 are determined as follows:

\[\dfrac{709}{1} = 709\]

\[\dfrac{709}{709} = 1\]

Therefore, 1 and 709 are the factors of 709.

Total Number of Factors of 709

For 709, there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 709. 

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 709 is given as:

Factorization of 709 is 1 x 709.

The exponent of 1 and 709 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 709 is 4. 2 is positive, and 2 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 709 by Prime Factorization

The number 709 is a prime 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 709 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 709, 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 709 can be expressed as:

709 = 1 x 709

Factors of 709 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 nine

For 709, the factor pairs can be found as:

1 x 709 = 709

The possible factor pairs of 709 are given as (1, 709).

All these numbers in pairs, when multiplied, give 709 as the product.

The negative factor pairs of 709 are given as:

-1 x -709 = 709 

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 and -709 are called negative factors of 709.

The list of all the factors of 709, including positive as well as negative numbers, is given below.

Factor list of 709: 1, -1, b, 709, and -709

Factors of 709 Solved Examples

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

Example 1

How many factors of 709 are there?


The total number of Factors of 709 is 4.

Factors of 709 are 1 and 709.

Example 2

Find the factors of 709 using prime factorization.


The prime factorization of 709 is given as:

709 $\div$ 709 = 1 

So the prime factorization of 709 can be written as:

709 x 1 = 709

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