A prime number is a number that can be divided only by 1 and itself. That is the number has exactly two factors.
For example, 13 is a prime number because 13 can only be divided evenly by 1 and 13.
If the number has more than two factors, we say that the number is composite.
For instance, 12 is a composite number because 12 can be divided by numbers other than 1 and 12, such as 2, 3, and 4.
1 is neither prime nor composite because it has only one factor. According to the definition, a number must have at least 2 factors before it can be prime or composite.
Notice also that 2 is the only number that is even and prime at the same time.
How many numbers less than 100 are prime?
You can use the definition to test every single number. It is somewhat time-consuming.
As a shortcut, you can use a method called Sieve of Eratosthenes, a famous Greek mathematician.
Here is his method:
Make a list of all numbers from 1 to 100
Start by crossing out 1 because it is not prime. Then,circle the next number after 1 that is prime, which is 2
Cross out all the multiples of 2 until you get to 100, such as 2, 6,8, 10, 12...
Look for the next number after 2 that is prime. That number is 3.Circle 3 and cross out all multiples of 3, such as 6, 9,12, ...
Repeat the process with 5 and 7. After you are done, you should find 25 prime numbers.
Every composite number can be written as the product of prime numbers. When a number is written as the product of primes number, we call the expressed product prime factorization
For instance, do the prime factorization of 40 and 24.
let us start with 40
start by dividing 40 by 2, you get 40 = 2 times 20
Divide 20 by 2 again because 20 can be divided by 2. You get 20 = 2 times 10
So far,we have 40 = 2 times 2 times 10
Divide 10 by 2 to get 10 = 2 times 5.
5 is prime,so you are done!
Thus, 40 = 2 times 2 times 2 times 5
Find prime factorization for 63.
63 cannot be divided by 2, so try the next number after 2, which is 3.
63 divided by 3 is 21, so 63 = 3 times 21
21 can be divided by 3 once again to get 7, so 21 = 3 times 7. 7 is prime, so you are done!
Thus, 63 = 3 times 3 times 7.
Use this prime calculator below to verify if a number is prime or not.
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