The factors of 101 are the numbers that can divide the original number completely. When multiplied in pair, the factors produce the original number and hence called pair factors. The factors of 101 are 1 and 101. Since 101 is a prime number, therefore it has only two factors. To find the factors of a number, 101, we will use the factorization method.
In the factorization method, first consider the numbers, 1 and 101 as factors of 101 and continue with finding the other pair of 101 which gives the results as an original number. To understand this method in a better way, read the article below to find the factors of 101 in pairs. Also, the prime factor of 101 is discussed here.
Table of Contents:
- What are the Factors of 101?
- Pair Factors of 101
- Factors of 101 by Division Method
- Prime Factorization of 101
- Solved Examples
- FAQs
What are the Factors of 101?
The Factors of 101 are the numbers that divide 101 exactly without leaving a remainder. In other words, the numbers 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.
Factors of 101: 1 and 101. Prime Factorization of 101: 1×101 (or) 101^{1}. |
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) |
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 101^{1}.
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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Examples
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.
Learn more about factors and prime factors of 101 and other numbers by downloading BYJU’S – The Learning App for a better experience and clarification.
Frequently Asked Questions on Factors of 101
What are the factors of 101?
The factors of 101 are 1 and 101, as 101 is a prime number.
What is the prime factorization of 101?
The prime factorization of 101 is 1 × 101 or 101^{1}.
Write down the positive and negative pair factors of 101?
The positive and negative pair factors of 101 are (1, 101) and (-1, -101) respectively.
Is 2 a factor of 101?
No, 2 is not a factor of 101, as it leaves the remainder 1.
Is 101 a factor of 101?
Yes, 101 is a factor of 101. If 101 is divisible by 101, it leaves a remainder 0.