Factors of 233: Prime Factorization, Methods, and Examples

The factors of 233 are the numbers that produce 233 as the product when multiplied together. The number 233 is a prime number so it only has 2 factors. 

Factors Of 233

These factors also give zero as the remainder and can be both positive as well as negative. 

Factors of 233

Here are the factors of number 233.

Factors of 233: 1, 233

Negative Factors of 233

The negative factors of 233 are similar to its positive factors, just with a negative sign.

Negative Factors of 233: -1 and -233

Prime Factorization of 233

The prime factorization of 233 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 233

In this article, we will learn about the factors of 233 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 233?

The factors of 233 are 1 and 233. All of these numbers are the factors as they do not leave any remainder when divided by 233.

The factors of 233 are classified as prime numbers. The prime factors of the number 233 can be determined using the technique of prime factorization.

How To Find the Factors of 233?

You can find the factors of 233 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 233, create a list containing the numbers that are exactly divisible by 233 with zero remainders. One important thing to note is that 1 and 233 are the 233’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 233 are determined as follows:

\[\dfrac{233}{1} = 233\]

\[\dfrac{233}{233} = 1\]

Therefore, 1 and 233 are the factors of 233.

Total Number of Factors of 233

For 233 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 233. 

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 233 is given as:

Factorization of 233 is 1 x 233

The exponent of 1 and 233 is 1.

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

Therefore, the total number of factors of 233 is 4. 2 are positive and 2 factors are negative.

Important Notes

Here are some important 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 233 by Prime FactorizationFactor of 233 by Prime Factorization

The number 233 is a prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 233 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 233, start dividing by its smallest 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 233 can be expressed as:

 233 = 1 x 233

Factors of 233 in PairsFactor of 233 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 of the given numbers.

For 233, the factor pairs can be found as:

1 x 233 = 233 

The possible factor pair of 233 is given as (1, 233).

All these numbers in pairs, when multiplied, give 233 as the product.

The negative factor pairs of 233 are given as:

-1 x -233 = 233 

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 -233 are called negative factors of 233.

The list of all the factors of 233 including positive as well as negative numbers is given below.

Factor list of 233: 1, -1, 233, and -233

Factors of 233 Solved Examples

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

Example 1

How many factors of 233 are there?


The total number of Factors of 233 is 2.

Factors of 233 are 1 and 233.

Example 2

Find the factors of 233 using prime factorization.


The prime factorization of 233 is given as:

233 $\div$ 233 = 1 

So the prime factorization of 233 can be written as:

1 x 233 = 233 

Factors of 232|Factors List| Factors of 234