Factors of 106: Prime Factorization, Methods, and Examples

The factors of 106 are the numbers from which 106 is completely divisible. In other words, factors of 106 are the numbers that yield zero as a remainder when 106 is divided from them.

Factors Of 106

The number 106 is an even composite number which means that it consists of multiple factors. In this article, we will evaluate the various factors of 106 and will see how to determine them. 

Factors of 106

Here are the factors of number 106.

Factors of 106: 1, 2, 53, 106

Negative Factors of 106

The negative factors of 106 are similar to its positive factors, just with a negative sign.

 Negative Factors of 106: -1, -2, -53 and -106

Prime Factorization of 106

The prime factorization of 106 is the way of expressing its prime factors in the form of a product.

Prime Factorization: 2 x 53

In this article, we will learn about the factors of 106 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 106?

The factors of 106 are 1, 2, 53, and 106. All of these numbers are the factors as they do not leave any remainder when divided by 106.

The factors of 106 are classified as prime numbers and composite numbers. The prime factors of the number 106 can be determined using the technique of prime factorization.

How To Find the Factors of 106?

You can find the factors of 106 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 106, create a list containing the numbers that are exactly divisible by 106 with zero remainders. One important thing to note is that 1 and 106 are the 106’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 106 are determined as follows:

\[\dfrac{106}{1} = 106\]

\[\dfrac{106}{2} = 53\]

\[\dfrac{106}{53} = 2\]

\[\dfrac{106}{106} = 1 \]

Therefore, 1, 2, 53, and 106 are the factors of 106.

Total Number of Factors of 106

For 106 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 106. 

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 106 is given as:

Factorization of 106 is 1 x 2 x 53.

The exponent of 1, 2, and 53 is 1.

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

Therefore, the total number of factors of 106 is 8. 

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 106 by Prime FactorizationFactor of 106 by Prime Factorization

The number 106 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 106 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 106, 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 106 can be expressed as:

106 = 2 x 53

Factors of 106 in PairsFactor of 106 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 106, the factor pairs can be found as:

1 x 106 = 106 

2 x 53 =106 

The possible factor pairs of 106 are given as (1, 106) and(2, 53).

All these numbers in pairs, when multiplied, give 106 as the product.

The negative factor pairs of 106 are given as:

 -1 x -106 = 106 

-2 x-53 = 106 

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, -53, and -106 are called negative factors of 106.

The list of all the factors of 106 including positive as well as negative numbers is given below.

Factor list of 106: 1, -1, 2, -2, 53, -53, 106, and -106

Factors of 106 Solved Examples

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

Example 1

How many factors of 106 are there?

Solution

The total number of Factors of 106 is 4.

Factors of 106 are 1, 2, 53, and 106.

Example 2

Find the factors of 106 using prime factorization.

Solution

The prime factorization of 106 is given as:

106 $\div$ 2 = 53 

53 $\div$ 53 = 1 

So the prime factorization of 106 can be written as:

2 x 53 = 106

Factors of 105|Factors List| Factors of 107