Factors of 8: Method, Total Number of Factors

What do we mean by Factors of 8?

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 8 i.e, the numbers which completely divide 8 are 1, 2, 4, 8. Therefore 8 has a total of 4 factors.

Factors of 8 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{8}{1}=8, Therefore  1 and 8 will be the factors of 8.

Now we’ll do it with numbers greater than one, \frac{8}{2}=4

Therefore the factors of 8 are 1, 2, 4, 8.

Factors of 8 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 will write 8 as 2 ×  2 × 2.     

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 8 into its prime factors.
8 can be written with prime factorization as-

⇒ 8 =  2 × 2 × 2.

Factors of 8 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 8  –

1 × 8 = 8

2 × 4 = 8

Therefore the Pair factors of 8 are (1,8) and (2,4).

Factors of a number can be negative too but only when they are in pairs and negative as when we multiply the two numbers we get the result as 8.

−1 × −8 = 8

−2 × −4 = 8

Therefore the negative Pair factors of 8 are (−1,−8) and (−2,−4).

Examples : 

1. Which of the following are factors of 8?

     – 2, 3, 4, 5, 6.

Solution:  2 and 4 are factors of 8 as they completely divide 8.
3, 5 and 6 are not factors of 8 as when we divide 8 from 3, 5 and 6 we do not get natural numbers.

\frac{8}{3}=2.67

\frac{8}{5}=1.6

\frac{8}{6}=1.34

2. Is 40 a factor of 8? 

Solution: No, 40 is not a factor of 8.

The highest factor of a number will be the number itself.

40 is a multiple of 8 as 8 x 5 = 40.

POINTS TO REMEMBER

• 1 is a factor of every number therefore it is known as a universal factor and the smallest factor of a number. 
• The highest factor of a number will be the number itself.
• A number having more than two factors is called a non-prime (composite) number. Therefore 8 is a composite number.