The factors of 101 are the numbers or integers that can divide the original number completely. When multiplied in pairs, the factors that produce the original number (i.e., 101) are called pair factors of 101.

The factors of 101 are 1 and 101. Since 101 is a prime number, therefore it has only two factors, where 101 is the largest factor.

The pair factors of 101 are (1, 101) and the prime factor is 101. To find the factors of a number, 101, we will use here factorization method and division method.  Click here to get factors of 1 to 100.

What are the Factors of 101?

The Factors of 101 are the numbers that divide 101 exactly without leaving a remainder. Factors will split 101 into equal parts or evenly.

In other words, the integers that are multiplied in pairs resulting in an original number 101 are the factors of 101. We know that 101 is a prime number and it has only two factors, such as 1 and the number itself. Hence, the factors of 101 are 1 and 101.

Pair Factors of 101

A pair of numbers that are multiplied together resulting in 101 is a pair factor of 101. The pair factors of 101 can be in positive pairs as well as in negative pairs. Thus, the positive and negative pair factors of 101 are given below:

Positive Pair Factor of 101:

Positive Factor of 101	Positive Pair Factor of 101
1 × 101	(1, 101)

Negative Pair Factor of 101:

Negative Factor of 101	Negative Pair Factor of 101
-1 × -101	(-1, -101)

How to Find Factors of 101?

To find the factors of 101, we have to list out the numbers that can evenly divide 101. Hence, there are only two such numbers available to us, they are 1 and 101. So, the factors are 1 and 101 for the whole number 101.

There are two methods to determine the factors:

• Division method
• Factorisation method

Let us have a look at other methods.

Factors of 101 by Division Method

In the division method, the factors of 101 can be found by dividing 101 by different integers. If the integer divides 101 exactly, then those integers are the factors of 101. 

• 101/1 = 101 (Factor =1  and Remainder =0)
• 101/101 = 1(Factor = 101 and Remainder =0)

If we divide 101 by any numbers other than 1 and 101, it leaves a remainder. Thus, the factors of 101 are 1 and 101.

Prime Factorization of 101

In the prime factorization of 101, the number 101 is written as the product of its prime factors. Now, let us discuss how to find the prime factors of 101.

• Take the pair factor of 101, say (1, 101).
• We know that the number 1 cannot be split further, and also 101 is a prime number.
• Now, write the number as the product of 1 and 101. Hence, 101 = 1 × 101
• Therefore, the prime factorization of 101 is 1 × 101 or 101¹.

Since the number 101 is a prime number and it possesses only two factors. i.e., the number 1 and the number itself 101. So the prime factorization of the number 101 is written as the number 101(itself).

We can easily find the number of factors by adding 1 to the exponent value of the prime number 101. So it becomes 1+1 =2.

Therefore, we can say the number 101 has two factors. The number 101 has no square factors and the simplified square root value of 101 is given as 10.04988 approximately.

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Solved Examples on Factors of 101

Example 1: Find the common factors of 101 and 100.

Solution:

The factors of 101 are 1 and 101.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

As 101 is a prime number, the common factor of 101 and 100 is 1 only.

Example 2: Find the common factors of 101 and 103.

Solution: Factors of 101 = 1, 101

Factors of 103 = 1, 103

As both the numbers 101 and 103 are prime numbers, the common factor of 101 and103 is 1.

Example 3: Find the common factors of 101 and 51.

Solution: The factors of 101 are 1 and 101.

The factors of 51 are 1, 3, 17 and 51.

Hence, the common factor of 101 and 51 is 1.

Example 4: What are the factors of 1001? How many factors in total it has?

Solution: The factors of 1001 are 1, 7, 11, 13, 77, 91, 143 and 1001.

Hence, there are total of eight factors of 1001.

Example 5: What are the factors of 111?

Solution: The factors of 111 are 1, 3, 37 and 111.

Example 6: What are the factors of 102?

Solution: The factors of 102 are 1, 2, 3, 6, 17, 34, 51 and 102.

Practice Questions

1. Which is the smallest factor of 101?
2. What is the value of 50 multiplied by the greatest factor of 101?
3. If 5 is a factor of 25, then 25 divided by 5 is equal to what number?

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