Factors of 101

Factors are simply the numbers that we use and multiply to get the parent number. Some numbers have one or more factorizations. If we take an example of 12, then it has 1,12,2,3,4,6 which, when multiplied appropriately, will give 12 as a result. 3 x 4 = 12, 2 x 6 = 12, 1 x 12 = 12, 12 x 1 = 12 are some pair factors of 12. 

To understand the factor of 101, you need to multiply two numbers and verify if the result is 101. The two numbers when multiplied with each other produce results as 101 are called factors of 101. When considering two numbers, you need to keep in mind that the number should be whole numbers irrespective of positive or negative. However, it cannot be a fraction or a decimal number. To understand vividly, you can go through the following example. 

Take a factor pair of number 42, which is (1, 42) and (-1, -42). Observe that while multiplying two negative numbers, we get a positive number. Thus, both positive and negative pairs considered are factors of 42. The best method to find the factor of 101 is the factorization method. 

Firstly, we need to consider the obvious numbers, aka 1 and 100, as factors of 101. Other factors that result in 101 should also be considered. Below is a complete explanation of how you can find the factors of 101. We will also discuss the prime factors. 

Prime Factorization of 101

Whilst finding the pair factors, you need to find two numbers when multiplied results original number 101. 

1 x 101 = 101 which proves 1, 101 is a pair factor of 101. 

101 x 1 = 101 which proves 101, 1 is a pair factor of 101. 

Thus, we can say that both (1, 101) and (101, 1) are a positive factor of 101. 

Negative factors can be found in two steps: 

-101 x -1 = 101 which proves -101 and -1 are negative factors of 101. 

-1 x -101 = 101 which proves -1 and -101 are negative factors of 101.


Thus, we can say that both (-1,-101) and (-101, -1) are negative pair factors of 101. 

Can the Factor be Only One Number? 

A factor of a number can never be one number though it can be multiplication of the same digit—for instance, 8. The 8 are multiples of 1, 8, 2, 4. When we consider 2, 2 x 2 x 2 = 8. Here 2 is not a factor of a number, but 2 x 2 x 2 is the factor of 8. Always prevent accidental over factorization. The prime factorization method is the best because you can avoid duplicitous multiplication of the numbers. When you consider the number 24, the smallest number that divides 24 is 2. The smallest part is not as important as a prime number. Finding a prime number will make your work simpler. Now 12 x 2=24. The number that factorizes 12 is 6, and 6 is 2 and 3. Thus, the prime factorization of 24 is 2 x 2 x 2 x 3. 

Solved Examples

Steps to Find the Factors of 101:

(image will be uploaded soon)

Finding prime factors of 101 can easily be done and this image shows 10 of them. 

Following are the Steps to Find the Factors of 101:

  • Write the number 101. 

  • Secondly, write the numbers which give results as 101. The numbers are 1 and 101, example: 1x101 = 101. 

  • We now know that the prime numbers 1 and 101 are the factors that cannot be further factored. 

  • The factors, therefore, are 101 and 1. 

Prime Factors: 

We know that 101 is a prime number and has only two factors, i.e., 1 and 101. The number one and the number itself when are factors are called prime numbers. So we can conclude that prime factorization of 101 is the number itself. The number of factors can be found by adding one exponentially to prime number 101. By adding, it becomes 1+1= 2. Thus, it can be concluded that 101 has two factors, and 101 has no square factor. However, the square root, when simplified, is 10.0498756. 

Are Factors of a Number Necessarily Small or can be Big?

Factors are total numbers that, when divided appropriately, results in the parent number. There are a few numbers that have more than one factorization. When a number can be factored only once, then it is called prime factors. When you are done factoring with small numbers, then try bigger numbers until you find something. If the squares of the number are bigger than what you are dividing, then only numbers that are divisible are prime. If the prime numbers are not dividing and the square of your number is bigger, the remainder will be a smaller prime number. The number left is smaller than the prime numbers that are eliminated. The number that is remaining is the prime number. Keep in mind that the number 1 is not a prime number. 

What is the List of Factors of Some Common Numbers?

The list of common factors and their prime factors are as follow: 

Factors of 36                 Factors of 68

Factors of 12                 Factors of 63

Factors of 72                 Factors of 215

Factors of 18                 Factors of 216

Factors of 98                 Factors of 17 

Factors of 80                 Factors of 150

Factors of 70                 Factors of 4

FAQ (Frequently Asked Questions)

1. What are the Factor Formulas?

There are three types of factor formulas: 

  1. Number of factors 

  2. Product of factors 

  3. Sum of factors 

When you assume a number A as a natural number, and you need to find the factor of T. By the prime factorization method, we can convert T into a product of prime numbers. We can also find prime numbers by simply finding the factors of a number. We can represent as follows.

2.  How can we Calculate the Factors of Large Numbers?

In order to calculate the factor of prime numbers of large numbers first, you have to divide the number with the least prime number like 2. In case it is not divisible by 2, then you can check other one-digit numbers. For instance, if we take 1420. When you find the pair of two numbers that give the product, you stop the process. The positive factors of 1420 will be 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710 and 1420. When we consider only prime numbers, then we call it prime factorization of that number.