Factors of 101: Prime Factorization, Methods, and Examples

101 is a prime number. It can be factored into only two numbers 1 and 101. The factors of 101 are the numbers that are exactly divisible by 101. Due to its prime nature, it cannot be divided by any other number except for 1 and 101.

Factors Of 101

Factors of 101

Here are the factors of number 101.

Factors of 101: 1, 101

Negative Factors of 101

The negative factors of 101 are similar to its positive factors, just with a negative sign.

Negative Factors of 101: -1 and -101

Prime Factorization of 101

The prime factorization of 101 is a way of expressing a number’s prime factors in terms of its product.

Prime Factorization: 1 x 101

In this article, we will learn about the factors of 101 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 101?

The factors of number 101 are 1 and 101. 101 is a prime number with two factors and when divided by these two remainders is zero.

101 is an odd number therefore it cannot be divided by 2 as well. 

How To Find the Factors of 101?

You can find the factors of 101 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 101, create a list containing the numbers that are exactly divisible by 101 with zero remainders. One important thing to note is that 1 and 101 are the 101’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 101 are determined as follows:

\[\dfrac{101}{1} = 101\]

\[\dfrac{101}{101} = 1\]

Therefore the only factors of 101 are 1 and 101.

Total Number of Factors of 101

For 101 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 101

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 101 is given as:

Factorization of 101 is 1 x 101.

The exponent of 1 and 101 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 101 is 4. 2 are positive and 2 factors are negative.

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 101 by Prime FactorizationFactor of 101 by Prime Factorization

The number 101 is a prime number. 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 101 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 101, 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 101 can be expressed as:

101 = 1 x 101 

Factors of 101 in PairsFactor of 101 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.

101 is a prime number with only two factors so it has only a 1-factor pair given as (1, 101).

Both of these numbers when multiplied results in 101.

The negative factor pair of 101 is (-1, -101),

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 and -101 are called negative factors of 101.

The list of all the factors of 101 including positive as well as negative numbers is given below.

Factor list of 101: 1, -1, 101, and -101

Factors of 101 Solved Examples

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

Example 1

Find the sum of factors of 101.

Solution

Factors of 101 are 1 and 101.

The sum of its factor is 101 + 1 = 102.

Example 2

Find the factors of 101 using prime factorization.

Solution

The prime factorization of 101 is given as:

 101 $\div$ 1 = 101 

So the prime factorization of 101 can be written as:

1 x 101 = 101

Factors of 100|Factors List |Factors of 102