What Are Composite Numbers? Definition, Examples & Importance
A positive integer that can be generated by multiplying two smaller positive integers is a composite number. All composite numbers can be written as the product of two or more primes. For example, an integer 21 is a composite number as it is the product of the two smaller integers 3 and 7.
List of Composite Numbers from 1 to 100
The composite numbers up to 100 are listed below.
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.
There are 74 numbers between the 1 to 100 composite numbers.
Odd and Even Composite Numbers
Odd composite numbers are all the odd integers that are not prime.
9, 15, 21, 25, 27, etc, are examples of composite odd numbers.
The smallest odd composite number is 9.
Even composite numbers are all even numbers and are not prime.
4, 6, 8, 10, 12, 14, 16, etc. are examples of even composite numbers.
The smallest even composite number is 4.
Solved Problems on Composite Numbers
1: How Many Composite Numbers Are There Between 1 to 50?
Ans: There are 34 composite numbers between 1 to 50 which are as follows:
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.
2. What are the Composite Numbers from 1 to 100? Represent them on a Composite Number Chart.
Ans: There are 74 composite numbers up to 100 which are represented in the composite number chart as follows:
Here the numbers in red color are composite numbers up to 100.
3. Write the Smallest Odd Composite Number?
Ans: The smallest odd composite number is 9.
4. List the First Five Odd Composite Numbers.
Ans: The first five odd composite numbers are as follows: 9, 15, 21, 25, 27.
According to basic Math, composite numbers are those numbers that have more than two factors present. The composite numbers or what is also commonly called the composites are the opposite of prime numbers which consists of only two factors and no more than that. When we say two factors there will be 1 and the other number present. All those numbers that are not prime numbers will be categorized as composite numbers. For you to better understand composite numbers and how they are found, here is a List of Composite Numbers from 1 to 100 via Vedantu that you can access and learn more about. This helps you to understand the composite numbers and their purposes in various mathematical equations.
Properties of Composite Numbers That Distinguish Them From Other Numbers:
Composite numbers are only those numbers that have more than two factors.
Composite numbers are also considered to be evenly divisible by the set of factors.
It is seen that each of the composite numbers is a factor of itself apart from 1 being the common factor.
The smallest of all composite numbers is 4 as it is divisible by 1, 2, and 4.
Each of the composite numbers will consist of at least two prime numbers that act as its factors. For example, if you check the composite number 10 it will have 2 and 5 as the prime numbers where the product of both will provide 10.
FAQs on Composite Numbers from 1 to 100: Full List Explained
1. What is the definition of a composite number in Maths?
A composite number is a positive integer that has more than two distinct factors. In other words, it is a whole number that can be divided evenly by numbers other than just 1 and itself. For example, the number 9 is a composite number because its factors are 1, 3, and 9.
2. What is the complete list of all composite numbers from 1 to 100?
The complete list of composite numbers from 1 to 100 is: 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.
3. How many composite numbers are there between 1 and 100?
There are 74 composite numbers between 1 and 100. Out of the first 100 integers, 1 is a unique number (neither prime nor composite), and there are 25 prime numbers. Therefore, the remaining 100 - 1 - 25 = 74 numbers are composite.
4. What is the main difference between prime and composite numbers?
The main difference lies in the number of factors they have.
- Prime Numbers: Have exactly two factors: 1 and the number itself. For example, 7 is prime (factors are 1 and 7).
- Composite Numbers: Have more than two factors. For example, 12 is composite (factors are 1, 2, 3, 4, 6, and 12).
5. What is the smallest even composite number and the smallest odd composite number?
The smallest even composite number is 4 (factors: 1, 2, 4). The smallest odd composite number is 9 (factors: 1, 3, 9).
6. Why are the numbers 0 and 1 considered neither prime nor composite?
The numbers 0 and 1 are special cases that do not fit the definitions of prime or composite numbers.
- The number 1: It has only one factor, which is itself. The definition of a prime number requires exactly two distinct factors, and a composite number requires more than two. Since 1 does not meet either criterion, it is unique.
- The number 0: It can be divided by any non-zero integer, meaning it has an infinite number of factors, which breaks the fundamental rules of factorization used to define prime and composite numbers.
7. Are all even numbers composite? Explain with an example.
No, not all even numbers are composite. The number 2 is an even number, but it is prime. This is because its only factors are 1 and 2, fitting the definition of a prime number. Every other even number greater than 2 is composite because, in addition to being divisible by 1 and itself, it is also divisible by 2.
8. How is understanding composite numbers useful for learning other Maths concepts?
Understanding composite numbers is a foundational skill essential for more advanced topics. It is crucial for:
- Prime Factorisation: Breaking down composite numbers into a product of their prime factors is a key technique in number theory.
- HCF and LCM: Finding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of numbers relies heavily on prime factorisation of composite numbers.
- Fractions: Simplifying fractions requires finding common factors, a skill directly related to understanding composite numbers.
9. How can you prove that an expression like 7 × 11 × 13 + 13 is a composite number without calculating the full value?
You can prove it is a composite number by using the distributive property to find its factors. The expression is 7 × 11 × 13 + 13. We can take 13 as a common factor: 13 × (7 × 11 + 1). This simplifies to 13 × (77 + 1) = 13 × 78. Since the original number can be expressed as a product of two integers (13 and 78), it has factors other than 1 and itself. Therefore, it is a composite number.
