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Factors of 933: Prime Factorization, Methods, and Examples
933 is a composite number consisting of 4 factors. 2 out of these four factors are prime numbers which makes the prime factorization of 933.
The smallest prime factor of 933 is 3, which is also the smallest odd prime number.
Factors of 933
Here are the factors of number 933.
Factors of 933: 1, 3, 311, and 933
Negative Factors of 933
The negative factors of 933 are similar to its positive aspects, just with a negative sign.
Negative Factors of 933: -1, -3, -311, and -933
Prime Factorization of 933
The prime factorization of 933 is the way of expressing its prime factors in the product form.
Prime Factorization: 3 x 311
In this article, we will learn about the factors of 933 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 933?
The factors of 933 are 1, 3, 311, and 933. These numbers are the factors as they do not leave any remainder when divided by 933.
The factors of 933 are classified as prime numbers and composite numbers. The prime factors of the number 933 can be determined using the prime factorization technique.
How To Find the Factors of 933?
You can find the factors of 933 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 933, create a list containing the numbers that are exactly divisible by 933 with zero remainders. One important thing to note is that 1 and 933 are the 933’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 933 are determined as follows:
\[\dfrac{933}{1} = 933\]
\[\dfrac{933}{3} = 311\]
\[\dfrac{933}{311} = 3\]
\[\dfrac{933}{933} = 1\]
Therefore, 1, 3, 311, and 933 are the factors of 933.
Total Number of Factors of 933
For 933, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 933.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- 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 933 is given as:
Factorization of 933 is 1 x 311 x 3.
The exponent of 1, 3, and 311 is 1.
Adding 1 to each and multiplying them together results in 933.
Therefore, the total number of factors of 933 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 933 by Prime Factorization
The number 933 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 933 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 933, 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 933 can be expressed as:
933 = 3 x 311
Factors of 933 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 933, the factor pairs can be found as:
1 x 933 = 833
3 x 311 = 933
The possible factor pairs of 933 are given as (1, 933) and (3, 311).
All these numbers in pairs, when multiplied, give 933 as the product.
The negative factor pairs of 933 are given as:
-1 x -933 = 933
-3 x -311 = 933
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, -311, and -933 are called negative factors of 933.
The list of all the factors of 933, including positive as well as negative numbers, is given below.
Factor list of 933: 1, -1, 3, -3, 311, -311, 933, and -933
Factors of 933 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 933 are there?
Solution
The total number of Factors of 933 is 4.
Factors of 933 are 1, 3, 311, and 933.
Example 2
Find the factors of 933 using prime factorization.
Solution
The prime factorization of 933 is given as:
933 $\div$ 3 = 311
311 $\div$ 311 = 1
So the prime factorization of 933 can be written as:
3 x 311 = 933