Factors of 18: Method, Total Number of Factors – Mindspark.

What do we mean by Factors of 18?

The factors of a number x  are the numbers that completely divide x with zero as a remainder. It means that if y divides x and the remainder is 0 then we say that y is a factor of x.

Factors of 18 i.e, the numbers which completely divide 18 are 1, 2, 3, 6, 9, 18. Therefore 18 has a total of 6 factors.

Factors of 18 by Division Method

The easiest way to calculate the factors of any number is by first dividing the number by its smallest factor. So the number which will divide the number completely and the quotient will also be the factor( This is also known as Pair of the factors). We will repeat this process till we find all the factors.

We know that 1 is the factor of every number, so 

\frac{18}{1} = 18, therefore  1 and 18 will be the factors of 18. Now we’ll do it with numbers greater than one.

\frac{18}{2} = 9

\frac{18}{3} = 6 

Therefore the factors of 18 are 1, 2, 3, 6, 9, 18.

Factors of 18 by Tree Method

The tree method is also known as Prime Factorisation. Prime Factorisation of a number means the way of writing the numbers by using its prime factors. For example, we can write 18 as 2 × 3 × 3.

We call it a tree method because the number of which we have to find the factors is the highest factor of itself (highest branch), the rest of the factors are lower than the number and when we simplify it we get the prime numbers (which are one of the smallest factors of the number) and this forms a shape like a tree as we are branching out 18 into its prime factors.

18 can be written with prime factorisation as- 

   18=2 \times 3^{2}

⇒ 18 = 2 × 3 × 3.

Factors of 18 in the form of Pairs

We can write the factors in the form of pairs. The pair means that when we will multiply the two numbers well get the result as 18 –

1 × 18 = 18

2 × 9 = 18

3 × 6 = 18

Therefore the Pairs factor of 18 are (1, 18),(2, 9),(3, 6).

Factors of a number can be negative too but only when they are in pairs and negative Since, when we multiply the two negative numbers we get a positive number and in this case the result as 18.

−1 × −18 = 18

−2 × −9 = 18

−3 × −6 = 18

Therefore the negative Pairs factor of 18 are (−1, −18),(−2, −9),(−3, −6).