Composite number is a positive integer greater than 1 that is not a prime number. In other words, a composite number has more than two factors (1 and itself).
What are Composite Number?
Composite numbers are numbers that can be divided by numbers other than 1 and themselves. For example, 4 is a composite number because it can be divided by 1, 2, and 4. Prime numbers, like 2, 3, 5, and 7, can only be divided by 1 and the number itself, so they are not composite.
Composite numbers are numbers that can be divided by numbers other than 1 and themselves. Example - 6, 8, ..., etc.
What is the Meaning of Composite Number?
A composite number is a number that can be formed by multiplying two smaller numbers together. This means, it has more than two factors (other than 1 and itself). For example, 4 is a composite number because it’s made by multiplying 2 and 2. Other examples are 6 (which is 2 times 3), 8 (which is 2 times 4), and 9 (which is 3 times 3).
Composite Number in Given Range
Identifying composite numbers within a specified range of integers, greater than one and having divisors other than one and themselves, using efficient algorithms and strategies.
First 10 Composite Numbers
The first 10 composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18
Composite Numbers 1 to 100
Here are the list of composite numbers from 1 to 100:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Composite Numbers Chart
History of Composite Numbers
Composite numbers, integers greater than one that can be divided by numbers other than 1 and themselves, have been a fundamental concept in mathematics since ancient times. The ancient Greek mathematicians, particularly Euclid, explored the properties of composite numbers as part of their study of number theory.
Euclid’s Elements, written around 300 BCE, contains some of the earliest known definitions and proofs related to composite numbers. Euclid proved that there are infinitely many composite numbers, a foundational result in number theory.
Properties of Composite Numbers
Composite numbers, which are integers greater than one that can be divided by numbers other than 1 and themselves, exhibit several interesting properties:
- Divisibility: Composite numbers are divisible by at least one number other than 1 and themselves.
- Factorization: Every composite number can be expressed as the product of two or more prime numbers. This is known as the fundamental theorem of arithmetic. For example, the composite number 12 can be factorized as 2 * 2 * 3.
- Multiplicity of Factors: Composite numbers have multiple factors. The number of factors a composite number has depends on its prime factorization.
- Notation: Composite numbers are often represented using a factorization notation, where the number is expressed as a product of its prime factors. For example, 30 is represented as 2^1 * 3^1 * 5^1.
- Relationship with Prime Numbers: Composite numbers are the opposite of prime numbers. While prime numbers have exactly two distinct factors, composite numbers have more than two factors.
- Applications: Composite numbers are used in various mathematical applications, such as cryptography, where the difficulty of factoring large composite numbers is leveraged for secure communication.
How to Find Prime Numbers?
The steps to find whether a Number is Composite Number or Prime Number:
- First, find all factors of the given number.
- If number has only two factors 1 and itself then the number will be Prime Number.
- If the number has more than two factors, then it will be composite number.
Example: How to find the number 10 is composite number?
Solution: Find all factors of 10, i.e. the factors of 10 are 1, 2, 5, and 10. The number 10 has four factors, so the number 10 is composite number.
Table of Composite Number with Prime Factorization
“Table of Composite Numbers with Prime Factorization” displays a list of composite numbers within the range of 20 to 40, along with their prime factorization. The prime factorization is the expression of the number as a product of its prime factors. This table provides a clear and organized view of these composite numbers, to understand their prime factorization patterns and relationships between numbers within the specified range.
Here is a table displaying composite numbers from 20 to 40 along with their prime factorization:
Composite Number | Prime Factorization |
---|---|
20 | 2 x 2 x 5 |
21 | 3 x 7 |
22 | 2 x 11 |
24 | 2 x 2 x 2 x 3 |
25 | 5 x 5 |
26 | 2 x 13 |
27 | 3 x 3 x 3 |
28 | 2 x 2 x 7 |
30 | 2 x 3 x 5 |
32 | 2 x 2 x 2 x 2 x 2 |
33 | 3 x 11 |
34 | 2 x 17 |
35 | 5 x 7 |
36 | 2 x 2 x 3 x 3 |
38 | 2 x 19 |
39 | 3 x 13 |
40 | 2 x 2 x 2 x 5 |
Prime or Composite Number
Prime or Composite Number is a fundamental concept in number theory. An integer is classified as either a prime number or a composite number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In contrast, a composite number is a natural number greater than 1 that is not prime, meaning it has factors other than 1 and itself.
Composite Number Examples
Example 1: Find if 102 is a composite number.
Solutions: The Factors of 102 are – 1, 2, 3, 6, 17, 34, 51, 102.
Prime Factorization of 102 are – 2 * 3 * 17.
Example 2: Find any two composite numbers between 20 and 30, and express them as a product of their prime factors.
Solutions: The composite numbers between 20 and 30 are – 20, 21, 22, 24, 25, 26, 27, 28, and 30.
The Factors of 24 are – 1, 2, 3, 4, 6, 8, 12, 24.
Prime Factorization of 24: 2 * 2 * 2 * 3
The Factors of 28 are – 1, 2, 4, 7, 14, 28.
Prime Factorization of 28: 2 * 2 * 7
Example 3: What is the prime factorization of 40.
Solutions: The Prime Factorization of 40 are: 2 x 2 x 2 x 5 i.e. 23 * 51.
Frequently Asked Questions on Composite Numbers
Q1. What is the Smallest Composite Number?
Ans. The smallest composite number is 4.
Q2. Is 1 a Composite Number?
Ans. No, 1 is not a composite number. It is neither prime nor composite.
Q3. What is the Smallest Odd Composite Number?
Ans. The smallest odd composite number is 9.
Q4. What is the Smallest Two Digit Composite Number?
Ans. The smallest two-digit composite number is 10.
Q5. Is 0 a Composite Number?
Ans. No, 0 is not a composite number.