[Maths Class Notes] on Is 101 A Prime Number? Pdf for Exam

What is a Factor of a Number?

Factors are basically the numbers that you multiply in order to get another number. Thus, the two basic numbers you require for getting the product answer are the factors of the said product. This concept can be really helpful in understanding ‘is 101 a prime number’ as well. For example: 

Answer: factors of 15 = 3 and 5 because 15 is a direct product you get when you multiply 3 and 5; 3 X 5.

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The concept of factors is very important to understand the basic difference between Prime Numbers and Composite Numbers and to determine whether a number is a prime or not. This concept would help you get the answer to the question of ‘is 101 a prime number?’ easily.

Now, coming back to Prime numbers.

What Are Prime Numbers?

Similar to atoms being the building blocks of elements in Science, Prime Numbers are nothing short than building blocks in Mathematics. You can define a Prime Number as a whole number who can possess only 2 factors, 1 and the number itself. For example:

Well, 11 is a Prime Number because you can divide 11 by only two numbers: 1 and 11 itself. On the other hand, 8 is a composite number because for 8, you get more factors: 8 = 2 X 4, 1 X 8. The same concept applies to the logic behind ‘Is 101 prime or composite number?

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The first 10 Prime numbers in the number list are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Following the list, you can get an answer to the question also, ‘is 101 a prime number.’?

Example

2 = 1 x 2; the only factors of 2 are 1 and 2;

3 = 1 x 3; the only factors of 3 are 1 and 3;

5 = 1 X 5, the only factors of 5 are 1 and 5;

7 = 1 X 7, the only factors of 7 are 1 and 7;

How to Find if the given number is a Prime Number?

To find out whether a given number is a prime number of not, you need to first try dividing it by 2. Did you get a whole number? If the answer is ‘Yes’, it cannot be a Prime Number. However, if you do not get a whole number on dividing by 2, try to divide it by prime numbers, i.e. 3, 5, 7, 11, etc. 

Table of Prime Number Upto 1,000

The table represents prime numbers between 1 and 1000.

Why Is 101 a Prime Number?

Based on the concepts mentioned above, it can be rightly said that 101 is a prime number. The reason being that 101  has only 2 factors, i.e., 1 and 101 itself.  Since you cannot get 101 as a product by multiplying any other two numbers, 101 is a Prime Number. You can also follow the below-mentioned steps to determine whether 101 is a prime or not. 

Step 1: Firstly, determine whether the ‘Units’ digit of the said number is either 2, 4, 6, 8, or in other words divisible by 2. If this is the case, then the given number is not a Prime Number. Since the ‘Units’ digit in 101 is not divisible by 2, it is a Prime Number.

Step 2: Check the divisibility of 101 with digits below 10.

Step 3: Check whether the sum of the digits in 101, i.e. 1 + 0 + 1 = 2 can be divided by 3.

Step 4: Take the factors test. Since 101 has no other factors than 1 and 101, it is Prime Number.

Solved Examples

Example 1: Is 63 A Prime Number?

Solution: No, 63 is Not a Prime Number.

63 is a multiple of 1, 3, 7, 9, 21. Thus, since it has more than two multiple, i.e. 1 and 63, it is not a prime number.

Example 2: Is 3 A Prime Number?

Solution: Yes, 3 is a Prime Number.

3 has only two multiple, i.e. 1 and 3, thus, it is a Prime Number.