Prime & Composite Numbers (2024)

Definition: A prime number is a whole number with exactly two integral divisors, $1$ and itself.

The number $1$ is not a prime, since it has only one divisor.

So the smallest prime numbers are:

$2, 3, 5, 7, \dots$

The number $4$ is not prime, since it has three divisors ( $1$ , $2$ , and $4$ ), and $6$ is not prime, since it has four divisors ( $1$ , $2$ , $3$ , and $6$ ).

Definition: A composite number is a whole number with more than two integral divisors.

So all whole numbers (except $0$ and $1$ ) are either prime or composite.

Example:

How can you tell if a number is prime?

First of all, here are some ways to tell if a number is NOT prime:

Any number greater than $2$ which is a multiple of $2$ is not a prime, since it has at least three divisors: $1$ , $2$ , and itself. (This means $2$ is the only even prime.)

Any number greater than $3$ which is a multiple of $3$ is not a prime, since it has $1$ , $3$ and itself as divisors. (For example, $303$ is not prime, since $303 \div 3 = 101$ .)

Any number which is a multiple of $4$ is also a multiple of $2$ , so we can rule these out.

Any number greater than $5$ which is a multiple of $5$ is not a prime. (So the only prime number ending with a $0$ or $5$ is $5$ itself.)

Any number which is a multiple of $6$ is also a multiple of $2$ and $3$ , so we can rule these out too.

You can continue like this... basically, you just have to test for divisibility by primes!

FAQs

Prime & Composite Numbers? ›

A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer. 1 is not a prime or composite number.

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What are composite and prime numbers? ›

A prime number has exactly two factors so 1 isn't prime. A composite number has more than 2 factors, so 1 isn't composite.

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What is prime number and composite numbers 1 to 100? ›

So all the prime numbers that come within the range of 1 to 100 can be listed as, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The remaining numbers in the range of 1 to 100 are composite numbers between 1 and 100.

Is 7 a prime or composite number? ›

Yes, 7 is a prime number. The number 7 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 7 has exactly two factors, i.e. 1 and 7, it is a prime number.

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What are prime and composite numbers Year 6? ›

prime numbers: a whole number higher than 1 that is only divisible by itself and 1. composite numbers: a whole number that is divisible by numbers other than itself and 1, for example, 4 is divisible by 2 as well as 1 and itself.

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How to know if a number is prime or composite quickly? ›

A prime number is the one that has only two factors and a composite number has more than two factors. A factor is a value, that can divide a number or an expression evenly.

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How do you identify a composite number? ›

Definition 1: In Mathematics, composite numbers are numbers that have more than two factors. Definition 2: The numbers which can be generated by multiplying the two smallest positive integers and contain at least one divisor other than the number '1' and itself are known as composite numbers.

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How do you explain a prime number? ›

A prime number is a whole number greater than 1 with only two factors – itself and 1. A prime number cannot be divided by any other positive integers without leaving a remainder, decimal, or fraction. An example of a prime number is 13. Its only divisors are 1 and 13.

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What is the smallest composite number? ›

All even numbers except 2 are composite numbers. 4 is the smallest composite number. Each composite number can be written as a product of two or more primes. Composite numbers are divisible by other composite numbers.

Why is 1 not a prime number? ›

The answer to this lies in the definition of prime numbers itself. For a number to be called as a prime number, it must have only two positive factors. Now, for 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number.

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Are all odd numbers prime? ›

Primes are always greater than 1 and they're only divisible by 1 and themselves. They cannot be made by multiplying two other whole numbers that are not 1 or the number itself. Another fact to keep in mind is that all primes are odd numbers except for 2. Prime numbers include: 2,3,5,7,11,13,17,19… and so on.

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Why is 2 a prime number? ›

According to the definition of prime numbers, any whole number which has only 2 factors is known as a prime number. Now, the factors of 2 are 1 and 2. Since there are exactly two factors of 2, it is a prime number.

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What is the trick to find prime numbers? ›

To find whether a larger number is prime or not, add all the digits in a number, if the sum is divisible by 3 it is not a prime number. Except 2 and 3, all the other prime numbers can be expressed in the general form as 6n + 1 or 6n - 1, where n is the natural number.

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What is a composite number example? ›

All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers. For example, 6 is a composite number because it is divisible by 1, 2, 3 and even by 6.

What are composite numbers 1 to 1000? ›

Odd Composite Numbers from 1 to 1000

9	15	27
51	55	65
87	91	99
121	123	133
153	155	165

29 more rows