banner

Factors of 816: Prime Factorization, Methods, and Examples

The factors of 816 are those numbers that leave zero as the residue when divided by 816. These figures divide 616 equally. The composite number 816 has an even number of 20 positive and 20 negative elements. 

The article provides more information on the factorization technique.

Factors of 816

Here are the factors of number 816.

Factors of 816:  1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408 and 816

Negative Factors of 816

The negative factors of 816 are similar to their positive aspects, just with a negative sign.

Negative Factors of 816:  -1, -2, -3, -4, -6, -8, -12, -16, -17,- 24, -34, -48, -51, -68, -102, -136, -204, -272, -408 and -816

Prime Factorization of 816

The prime factorization of 816 is the way of expressing its prime factors in the product form.

Prime Factorization: 24 x 31 x 171

In this article, we will learn about the factors of 816 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 816?

The factors of 816 are  1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408 and 816. These numbers are the factors as they do not leave any remainder when divided by 816.

The factors of 816 are classified as prime numbers and composite numbers. The prime factors of the number 816 can be determined using the prime factorization technique.

How To Find the Factors of 816?

You can find the factors of 816 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 816, create a list containing the numbers that are exactly divisible by 816 with zero remainders. One important thing to note is that 1 and 816 are the 816’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 816 are determined as follows:

\[\dfrac{816}{1} = 816\]

\[\dfrac{816}{2} = 408\]

\[\dfrac{816}{3} = 272\]

\[\dfrac{816}{4} = 204\]

\[\dfrac{816}{6} = 136\]

\[\dfrac{816}{8} = 102\]

\[\dfrac{816}{12} = 68\]

\[\dfrac{816}{16} = 51\]

\[\dfrac{816}{17} = 48\]

\[\dfrac{816}{24} = 34\]

\[\dfrac{816}{34} = 24\]

\[\dfrac{816}{48} = 17\]

\[\dfrac{816}{51} = 16\]

\[\dfrac{816}{68} = 12\]

\[\dfrac{816}{102} = 8\]

\[\dfrac{816}{136} = 6\]

\[\dfrac{816}{204} = 4\]

\[\dfrac{816}{272} = 3\]

\[\dfrac{816}{408} = 2\]

\[\dfrac{816}{816} = 1\]

Therefore,  1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408 and 816 are the factors of 816.

Total Number of Factors of 816

For 816, there are 20 positive factors and 20 negative ones. So in total, there are 40 factors of 816. 

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 816 is given as:

Factorization of 816 is 24 x 31 x 171.

The exponent of 2 is 4, 3 is 1, and 17 is 1.

Adding 1 to each and multiplying them together results in 40.

Therefore, the total number of factors of 816 is 40. 20 are positive, and 20 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 816 by Prime Factorization

The number 816 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 816 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 816, 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 816 can be expressed as:

816 = 24 x 31 x 171

Factors of 816 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 816, the factor pairs can be found as:

1 x 816 = 816

2 x 408 = 816

3 x 272 = 816

4 x 204 =816

6 x 136 = 816

8 x 102 = 816

12 x 68 = 816

16 x 51 = 816

17 x 48 = 816

24 x 34 = 816

The possible factor pairs of 816 are given as (1, 816),(2, 408),(3, 272),(4, 204),(6, 136),(8, 102),(12, 68), (16, 51),(17, 48), and (24, 34).

All these numbers in pairs, when multiplied, give 816 as the product.

The negative factor pairs of 816 are given as:

-1 x -816 = 816

-2 x -408 = 816

-3 x -272 = 816

-4 x -204 =816

-6 x -136 = 816

-8 x -102 = 816

-12 x -68 = 816

-16 x- 51 = 816

-17 x- 48 = 816

-24 x -34 = 816

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, -12, -16, -17,- 24, -34, -48, -51, -68, -102, -136, -204, -272, -408 and -816 are called negative factors of 816.

The list of all the factors of 816, including positive as well as negative numbers, is given below.

Factor list of 816: 1,-1, 2,-2, 3,-3,4, -4, 6,-6, 8,-8, 12,-12, 16,-16, 17,-17,24,-24, 34,-34, 48,-48, 51,-51, 68,-68, 102,-102, 136,-136, 204,-204, 272,-272, 408,-408, 816, and -816

Factors of 816 Solved Examples

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

Example 1

How many factors of 816 are there?

Solution

The total number of Factors of 816 is 40.

Factors of 816 are  1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408 and 816.

Example 2

Find the factors of 816 using prime factorization.

Solution

The prime factorization of 816 is given as:

816 $\div$ 2 = 408 

408 $\div$ 2 =204 

204 $\div$ 2 = 102 

102 $\div$ 2 = 51 

51 $\div$ 3 = 17

17 $\div$ 17 = 1 

So the prime factorization of 816 can be written as:

24 x 31 x 171 = 816

Factors of 815|Factors List| Factors of 817

5/5 - (5 votes)