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Factors of 792: Prime Factorization, Methods, and Examples

The factors of 792 are numbers that, when divided by 792, leave zero as the remainder. The given number’s factors can be positive and negative. 

Let we know more about factors of 792 in this article. 

Factors of 792

Here are the factors of number 792.

Factors of 792: 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, and 792.

Negative Factors of 792

The negative factors of 792 are similar to its positive aspects, just with a negative sign.

Negative Factors of 792: –1, -2, -3, -4, -6, -8, -9, -11, -12, -18, -22, -24, -33, -36, -44, -66, -72, -88, -99, -132, -198, -264, -396, and -792

Prime Factorization of 792

The prime factorization of 792 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 3 x 3 x 11

In this article, we will learn about the factors of 792 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 792?

The factors of 792 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, and 792. These numbers are the factors as they do not leave any remainder when divided by 792.

The factors of 792 are classified as prime numbers and composite numbers. The prime factors of the number 792 can be determined using the prime factorization technique.

How To Find the Factors of 792?

You can find the factors of 792 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 792, create a list containing the numbers that are exactly divisible by 792 with zero remainders. One important thing to note is that 1 and X are the X’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 X are determined as follows:

\[\dfrac{792}{1} = 792\]

\[\dfrac{792}{2} = 396\]

\[\dfrac{792}{3} = 264\]

\[\dfrac{792}{4} = 198\]

\[\dfrac{792}{6} = 132\]

\[\dfrac{792}{8} = 99\]

\[\dfrac{792}{9} = 88\]

\[\dfrac{792}{11} = 72\]

\[\dfrac{792}{12} = 66\]

\[\dfrac{792}{18} = 44\]

\[\dfrac{792}{22} = 36\]

\[\dfrac{792}{24} = 33\]

Therefore, 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, and 792 are the factors of 792.

Total Number of Factors of 792

For 792, there are twenty four positive factors and twenty four negative ones. So in total, there are 48 factors of 792. 

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 792 is given as:

Factorization of 792 is 1 x 2$^3$ x 3$^2$ x 11.

The exponent of 1, and 11 is 1 where as 2 is 3 and 3 is 2.

Adding 1 to each and multiplying them together results in 48.

Therefore, the total number of factors of 792 is 48. Twenty four are positive, and twenty four 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 792 by Prime Factorization

The number 792 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 792 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 792, 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 792 can be expressed as:

792 = 2 x 2 x 2 x 3 x 3 x 11

Factors of 792 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 792, the factor pairs can be found as:

1 x 792 = 792

2 x 396 = 792

3 x 264 = 792

 4 x 198 = 792

6 x 132 = 792

8 x 99 = 792

9 x 88 = 792

11 x 72 = 792

12 x 66 = 792

18 x 44 = 792

22 x 36 = 792

24 x 33 = 792

The possible factor pairs of 792 are given as (1, 792), (2, 396), (3, 264), (4, 198), (6, 132), (8, 99), (9, 88), (11, 72), (12, 66), (18, 44), (22, 36) and (24, 33).

All these numbers in pairs, when multiplied, give 792 as the product.

The negative factor pairs of 792 are given as:

1 x -792 = 792

-2 x -396 = 792

-3 x -264 = 792

 -4 x -198 = 792

-6 x -132 = 792

-8 x -99 = 792

-9 x -88 = 792

-11 x -72 = 792

-12 x -66 = 792

-18 x -44 = 792

-22 x -36 = 792

-24 x -33 = 792

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, -2, -3, -4, -6, -8, -9, -11, -12, -18, -22, -24, -33, -36, -44, -66, -72, -88, -99, -132, -198, -264, -396, and -792 are called negative factors of 792.

The list of all the factors of 792, including positive as well as negative numbers, is given below.

Factor list of 792: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 11, -11, 12, -12, 18, -18, 22, -22, 24, -24, 33, -33, 36, -36, 44, -44, 66, -66, 72, -72, 88, -88, 99, -99, 132, -132, 198, -198, 264, -264, 396, -396, 792, and -792

Factors of 792 Solved Examples

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

Example 1

How many factors of 792 are there?

Solution

The total number of Factors of 792 is 48.

Factors of 792 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, and 792.

Example 2

Find the factors of 792 using prime factorization.

Solution

The prime factorization of 792 is given as:

792 $\div$ 2 = 396 

396 $\div$ 2 = 198

198 $\div$ 2 = 99

99 $\div$ 3 = 33

33 $\div$ 3 = 11

11 $\div$ 11 = 1 

So the prime factorization of 792 can be written as:

2 x 2 x 2 x 3 x 3 x 11 = 792

Factors of 791|Factors List| Factors of 793

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