Table of Contents
Even Numbers
An even number is an integer that is divisible by 2. The following are all even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
Odd Numbers
An odd number is a number that is not evenly divisible by two. This means that the number cannot be divided by two without leaving a remainder. The number one is the only exception to this rule, as it is evenly divisible by two.
Some of the most common odd numbers include 3, 5, 7, and 9. These numbers are all prime numbers, meaning that they can only be divided by themselves and one.
Prime Numbers
Prime numbers are numbers that are only divisible by themselves and one. They are the building blocks of all numbers and can be thought of as the foundation of mathematics. Prime numbers are generally considered to be the most fundamental and important numbers in mathematics.
In mathematics, prime numbers are used to divide, factor, and simplify equations. They are also used to create algorithms and to solve complex problems. Prime numbers are essential to cryptography and data security. They are used to generate strong and secure keys for encryption, which is the process of scrambling data so it can’t be accessed without a key.
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.
Composite Numbers
A composite number is a number that can be divided evenly by two or more numbers other than 1 and itself. For example, the number 12 can be divided evenly by 2, 3, 4, and 6. The number 15 can be divided evenly by 3 and 5. The number 21 can be divided evenly by 3, 7, and 11.
The number 1 is not a composite number because it can only be divided evenly by 1 and itself. The number 2 is not a composite number because it can only be divided evenly by 1 and itself. The number 4 is not a composite number because it can only be divided evenly by 1 and itself. However, the number 3 is a composite number because it can be divided evenly by 2 and 1.
The number 9 is the smallest composite number because it can be divided evenly by 2, 3, and 9. The number 30 is the largest composite number because it can be divided evenly by 2, 3, 5, 10, and 15.
Composite numbers are important in mathematics because they are used to calculate the greatest common factor (GCF) and the least common multiple (LCM) of two or more numbers. The GCF of two or more numbers is the largest number that can be divided evenly by all of the numbers. The LCM of two or more numbers is the smallest number that can be divided evenly by all of the numbers.
Adding and Subtracting:
To add or subtract fractions, first find the LCD or Least Common Denominator. This is the smallest number that both fractions can be divided by without a remainder.
Then, multiply (or divide) the numerators and denominators of both fractions by the LCD.
Finally, add (or subtract) the numerators, and keep the denominator the same.
Here is an example:
To add 1/4 and 2/9, find the LCD, which is 36.
Then, multiply the numerators and denominators of both fractions by 36.
Finally, add the numerators, 1 + 2 = 3, and keep the denominator the same, 36.
So, the answer is 3/36.
Multiplying:
We multiply by 10 because we want to move the decimal point two places to the right.
So, 10.23 becomes 102.3
Test Your Skills with the Divisibility Test with the Following Examples:
1. Determine if 9 is divisible by 3.
9 is divisible by 3 because the remainder when 9 is divided by 3 is 0.
2. Determine if 9 is divisible by 2.
9 is not divisible by 2 because the remainder when 9 is divided by 2 is 1.
3. Determine if 12 is divisible by 4.
12 is divisible by 4 because the remainder when 12 is divided by 4 is 0.
How to Find a Number that is Prime or Composite?
To find a number that is prime, use a factorization chart to find all the prime numbers that multiply together to create the number in question. Then, cross out any composite numbers that are factors of the number. The number that is left is the prime number.
To find a number that is composite, use a factorization chart to find all the prime numbers that multiply together to create the number in question. Then, cross out any prime numbers that are factors of the number. The number that is left is the composite number.
Applications of Prime and Composite Numbers:
– Prime numbers can be used in cryptography, especially in the generation of random numbers.
– A composite number is the result of multiplying two prime numbers together. They are used in many number theoretic problems and investigations.
For more visit Co Prime Numbers – Definition, Properties and Solved Examples
