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Factors of 104: Prime Factorization, Methods, and Examples

The factors of 104 are the numbers that, when they act as divisors, give zero as a remainder. Not only do these numbers give zero as a remainder but they also yield a whole number quotient.

The factors of 104 can be determined through various methods such as prime factorization and the division method. In this article, we will be exploring all the ways through which these factors can be determined. 

Factors of 104

Here are the factors of number 104.

Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104

Negative Factors of 104

The negative factors of 104 are similar to its positive factors, just with a negative sign.

Negative Factors of 104: -1, -2, -4, -8, -13, -26, -52 and -104 \]

Prime Factorization of 104

The prime factorization of 104 is the way of expressing its prime factors in the form of its product.

Prime Factorization: 2 x 2 x 3 x13

In this article, we will learn about the factors of 104 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 104?

The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104. All of these numbers are the factors as they do not leave any remainder when divided by 104.

The factors of 104 are classified as prime numbers and composite numbers. The prime factors of the number 104 can be determined using the technique of prime factorization.

How To Find the Factors of 104?

You can find the factors of 104 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 104, create a list containing the numbers that are exactly divisible by 104 with zero remainders. One important thing to note is that 1 and 104 are the 104’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 104 are determined as follows:

\[\dfrac{104}{1} = 104\]

\[\dfrac{104}{2} = 52\]

\[\dfrac{104}{4} = 26\]

\[\dfrac{104}{8} = 13\]

\[ \dfrac{104}{13} = 8\]

\[ \dfrac{104}{26} = 4\]

\[ \dfrac{104}{52} = 2\]

\[ \dfrac{104}{104} = 1\]

Therefore, 1, 2, 4, 8, 13, 26, 52, and 104 are the factors of 104.

Total Number of Factors of 104

For 104 there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 104. 

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 104 is given as:

\[104 = 1 \times 2^{3} \times 13\]

The exponent of 1 and 13 is 1 while that of 2 is 3.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 104 is 16 where there are 8 positive factors and 8 negative factors.

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 which is the smallest prime factor.

Factors of 104 by Prime Factorization

The number 104 is composite. 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 104 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 104, 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 104 can be expressed as:

\[104 = 2^{3} \times 13\]

Factors of 104 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

For 104, the factor pairs can be found as:

\[ 1 \times 104 = 104 \]

\[ 2 \times 52 = 104 \]

\[ 4 \times 26 = 104 \]

\[ 8 \times 13 = 104 \]

The possible factor pairs of 104 are given as (1, 104), (2, 52), (4, 26), and (8, 13).

All these numbers in pairs, when multiplied, give 104 as the product.

The negative factor pairs of 104 are given as:

\[ -1 \times -104 = 104 \]

\[ -2 \times -52 = 104 \]

\[ -4 \times -26 = 104\]

\[ -8 \times -13 = 104 \]

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, -4, -8, -13, -26, -52 and -104 are called negative factors of 104.

The list of all the factors of 104 including positive as well as negative numbers is given below.

Factor list of 104: 1, -1, 2, -2, 4, -4, 8, -8, 13, -13, 26, -26, 52, -52, 104, and -104

Factors of 104 Solved Examples

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

Example 1

How many factors of 104 are there?

Solution

The total number of Factors of 104 is 8.

Factors of 104 are 1, 2, 4, 8, 13, 26, 52 and 104.

Example 2

Find the factors of 104 using prime factorization.

Solution

The prime factorization of 104 is given as:

\[ 104 \div 2 = 52 \]

\[ 52 \div 2 = 26 \]

\[ 26 \div 2 = 13\]

\[ 13 \div 13 = 1\]

So the prime factorization of 104 can be written as:

\[ 2^{3} \times 13 = 104 \]

Factors of 103|Factors List |Factors of 105

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