What are the factors of 18? The factors of 18 are 1,2,3,6,9. Factors are the number which divides a certain number into its exact with no decimals in the quotient. The numbers which are the result of factorization can be represented either equally or in pairs.
Primary factorization of 18.
Prime factorization is the formation of an operation in which a certain number is factorized in a way that the pairs or results formed are all prime numbers. In the case of 18, when it is factorized, the numbers attained should be prime numbers which are 2 and 3
2 x 2 x 3= 18
The numbers should be, however, taken from the smallest integers.
Composite numbers
Composite numbers are formed by multiplying two positive integers, and these integers are smaller numbers which are not the number itself and 1. 18 is a composite integer since it can be attained by multiplying smaller numbers other than 18 itself and 1.
Square number
Square numbers are those which, when taken, a square root gives a whole number. 18 cannot be a square number because its square root is 4.24. 16 is a square number because it is square root is 4.
Factors of 18
18 has six factors 1, 2, 3, 6, 9 and 18.
These factors are shown in pairs as
1 x 18
2 x 9
3 x 6
6 x3
9 x 2
18 x 1
Greatest Common Factor
Greatest Common Factor is found among two numbers. The two numbers are factorized, and then the resultant numbers are listed. The highest number is taken from each list, which is common in both results. If there are no common prime factors in two numbers, then the Greatest Common Factor is 1.
For example
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Finding the Greatest Common Factor of 14 and 16
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The prime factorization of 14 are 1, 2, 7, 14
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The prime factorization of 16 are 1, 2, 4, 8, 16
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The Greatest Common factors of 14 and 16 are 2 (other than 1)
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Finding the Greatest Common Factor of 15 and 17
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The prime factorization of 15 is 1, 3, 5, 15
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The prime factorization of 17 is 1, 17
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There is no Greatest Common Factor among 15 and 17 but 1
Least Common Multiple
The Least Common Multiple are two sets in which the smallest number that both the numbers share in their factorization.
For example
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The Least Common Multiple for 14 and 16
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The prime factorization of 14 are 1, 2, 7
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The prime factorization of 16 are 1, 2, 4, 8
The common numbers are cut down, which in this case are 1 and 2. While the rest of the numbers are multiplied to get the result which in this operation is 112
Factor tree
A factor tree is the representation of the factors and sub-factors graphically in which factorization is simplified. The numbers to be factorized are written in the tree, and their sub-factors are derived until many prime factors are derived.
Factors of -18
The negative 18 (-18) factors can be found by the same method as the positive 18 (+18). However, the answers will all have the negative (-) sign.
-1, -2, -3, -6, -9, -18
Whole number.
An integer that is not presented by fractions. The number 18 is a whole number. 18.5 can be presented in fractions, so it is not a whole number.
Divisibility rule
The divisibility rule is a set of rules determining if a number is divisible by a particular divisor. It is a shortcut in which you do not have to go through the division process altogether.
For example
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The numbers ending in 0, 2, 4, 6 or even numbers are divisible by 2
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346 is divisible by 2, giving the whole number answer 178
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345 is not divisible by 2, answering decimal 172.5
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The numbers whose sum is divisible by 3 are divisible by 3
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The sum of the number 15 is 1+5= 6, 6 is divisible by 3, so 15 is divisible by 3
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The sum of the number 14 is 1+4=5, 5 is not divisible by 3, so 14 is not divisible by 3
Summary
Mathematics may have complicated concepts, but once you grasp them, it will be very amusing to see how the numbers play with each other. In this article, we have shown the mathematical operations and concepts circulating the number 18. Therefore, more numbers can be factorized or taken through different concepts and operations to understand mathematics better. There are many other interesting rules of mathematics which can make calculations easier.
BODMAS rule
It stands for Brackets, pOwers, Division, Multiplication, Addition and Subtraction. This rule must be followed if there is a mathematical operation with more than one operation in different forms like brackets, addition, multiplication, etc.
First, take all the integers in the bracket and derive their answers. If there is more than one operation in the brackets, divide, multiply, add and subtract as per the operations mentioned.
5 + (5 x 6 – 15 / 3)
First, divide 15/3
5 + (5 x 6 – 5)
Now multiply
5 + (30 – 5)
Now subtract
5 + (25)
All operations in the bracket are solved.
We can do the operations outside the brackets now.
5 + 25
The answer to the whole operation is 30.
This rule also involves pOwers, which come after solving the integers inside the brackets. After the operations are solved the, if any power is mentioned outside the bracket, then it will be solved.
Not all operations need to have all the BODMAS factors in them. Maybe an operation you see will not have a division in it. So skip that part and after solving the brackets and powers, just do the multiplication. If there are no brackets in operation, then simply solve the powers and follow the rest of the DMAS.
In solving brackets, keep another thing in mind there are three types of brackets. Parenthesis, square brackets and curly brackets. They also follow an order in the BODMAS rule. In which the curly brackets are solved first. Second, comes the square brackets operations, and lastly, the parenthesis.