Table of Contents
Introduction
You are familiar with the factors of a number, that is, when you find the factors of those counting numbers that are greater than 1. There are many numbers in the number system that have exactly two factors: 1 and the number itself. They are known as prime numbers. Here is a list of prime numbers from 1 to 1,000.
Solved Examples
Example 1:
Is 40 a prime number?
Solution:
Find the factors of 40.
Factors of 40 = 1 , 2 , 4 , 5 , 8 , 10 , 20, and 40.
40 has more factors other than 1 and 40 (itself).
Hence, 40 is not a prime number.
Example 2:
Is 41 a prime number?
Solution:
Find the factor of 41.
\(41=41 \times 1\)
41 does not have factors other than 1 and 41 itself.
So, 41 is a prime number.
The number 1 is a factor of every other number.
For example:
\(6=6\times 1\)
\(12=12\times 1,\) and so on.
From these observations, one can say that 1 is a factor of every number.
Yes, every prime number, except 2, is an odd number.
The smallest and the only even prime number is 2.
Any number that is a multiple of two is called an even number.
You can identify even numbers by seeing their ones place.
An even number has the following digits in the ones place or ends with 0, 2 , 4, 6, 8.
A factor of any number is the exact divisor of that number. We can also say that a factor divides the number in such a way that the remainder is equal to zero.
For example:
Find the factors of 6.
Solution:
\(1 \times 6=6\)
From the above product, the exact divisors of 6 are found to be: 1 and 6.
\(2 \times 3=6\)
From the product, it can be said that 2 and 3 divide 6 exactly.
So 1, 2, 3, and 6 are the exact divisors of 6. They are called factors of 6.
Note that:
- Every number is a factor of itself, and
- 1 is a factor of every number.
The multiple of a number is a number that is obtained by multiplying one whole number by another whole number.
There are an infinite number of multiples of a number.
For example:
The first 10 multiples of 8 are:
8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , and 80