Factors of 8

What are the Factors of 8?

Factors of 8 is the product of such numbers which completely divide the given number 8. Factors of a given number have two values; they can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 3, 9 are the factors of 9. Hence we have 3 x 3 = 9 or 1 x 9 = 9. In this article, we will study the factors of 8, what are the factors of 8, what is the prime factorization of 8, factor tree of 8, and examples. Factor pairs of the number 8 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 8. 


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Factors of 8 Definition

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.


Factors of 8 are all the integers that can evenly divide the given number 8.

Now let us study how to calculate all factors of 8.


What are the Factors of 8?

According to the definition of factors of 8, we know that factors of 8 are all the positive or negative integers which divide the number 8 completely. So let us simply divide the number 8 by every number which completely divides 8 in ascending order till 8.

8 ÷ 1 = 8

8 ÷ 2 = 4

8 ÷ 3 = not divides completely

8 ÷ 4 = 2

8 ÷ 5 = not divides completely

8 ÷ 6 = not divides completely

8 ÷ 7 = not divides completely

8 ÷ 8 = 1


So all factors of 8: 1, 2, 4, and 8.


We know that factors also include negative integers hence we can also have, 

list of negative factors of 8: -1, -2, -4 and -8.


All Factors of 8 can be Listed as Follows

Positive Factors of 8

1, 2, 4 and 8

Negative Factors of 8

-1, -2, -4 and -8.


Hence 8 have total 4 positive factors and 4 negative factors.


All Factor Pairs of 8

All Factor Pairs of 8 are combinations of two factors that when multiplied together give 8.


List of all the positive pair factors of 8

1 x 8 = 8; (1, 8)

2 x 4 = 8; (2, 4)


So (1, 8), and ( 2, 4), are the positive pair factors of 8


As we know that Factors of 8 include negative integers too. 

List of all the negative pair factors of 8:

-1 x -8 = 8

-2 x -4 = 8

So (-1, -8), and ( -2, -4) are the negative pair factors of 8


Now we will study what is the prime factorization of 8.


What is the Prime Factorization of 8

According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime that is a number that divides by itself and only one. Hence we can list the prime factors from the list of factors of 8.


Or the other way to find the prime factorization of 8 is by prime factorization or by factor tree.


Now let us study prime factors of 8 by division method.


Prime Factors of 8 by Division Method

To calculate the prime factors of 8 by division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 8


Step 1: Divide 8 with 2

8 ÷ 2 = 4


Step 2: Now again divide 4 by 2

4 ÷ 2 = 2 


Step 3: Now again 2 is  divisible by 2

2 2 = 1


We get the quotient 1.


From the above steps, we get a prime factor of 8 as 2 x 2 x 2 = 23

Here is the factor tree of 8.


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Solved Examples

Example 1: Find the prime factors of 80.

Solution: 

       80 = 2 x 40

= 2 x 2 x 20

= 2 x 2 x 2 x 10

= 2 x 2 x 2 x 2 x 5


Factor tree (image will be uploaded soon)


Example 2: Factor tree for 1260

Solution:


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Facts:

  • A factor of any number is its exact divisor i.e it divides the given number exactly.

  • 1 is a common factor of every number.

  • Every factor of a number is always less than or equal to the original number.

  • The original number itself is the greatest factor.

FAQ (Frequently Asked Questions)

1. What is the Definition of Factors in Maths?

Answer: 

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. Factors of a given number have two values; they can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 3, 9 are the factors of 9. Hence we have 3 x 3 = 6 or 1 x 9 = 9.

2. What is Perfect Square?

Answer: A product of an integer with itself is said to be square or perfect square. Or in other words you can say that if any number is multiplied by itself it gives a perfect square.


For example 64 is a perfect square since it can be written as 64 = 8 x 8.

Perfect square is a number obtained by squaring two equal integers.


For testing if a given number is a perfect square or not we write the given number as the product of prime factors then we make pairs of the same factors.If there are factors all of which have a pair, then the given number is a perfect square.