 # Is 101 A Prime Number?

Every mathematical number can be divided into two categories: Prime number and Composite number. While Composite Numbers can be defined as whole numbers which possess more than two factors, the Prime Numbers are slightly different. It is very easy to find out if any given number is a prime number or not. You just need to find out an integer that can evenly divide the said number. However, the integer should not be 1 or the number itself. Now, coming to the question of is 101 a prime number?, the answer is ‘Yes’. Let us find out in detail about how and why is 101 a prime?

### 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:

• What will be the factors of 15?

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

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?

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

 1 2 3 5 7 9 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 953 967 971 977 983 991 997

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.