Factors of 8 | with Easy division and prime factorization

Factors of 8

Factors of 8 are the numbers that divide the number 8 without leaving any reminder, so these factors can’t be in fractions. There are 4 (four) factors of 8. The positive factors of 8 are 1, 2, 4, and 8. The positive pair factors of 8 are (1, 8) and (2, 4) and the negative pair factors of 8 are (-1, -8) and (-2, -4). 2 is the only prime factor of 8.

Factors of 8: 1, 2, 4 ,8

Negative Factors of 8: -1, -2, -4,-8

Prime Factors of 8: 2

Prime Factor of 8: 2 

Sum of Factors of 8: 1+2+4 +8=15

What are Factors of 8?

Factors of 8 are those numbers that completely divide it, leaving zero (0)  as the remainder. For example, 8 ÷ 1 leaves a remainder 0.

We get 8 as the quotient and 0 as the remainder. This indicates that 8 is divisible by 1 so 1 and 8 are the factor of 8. Let’s see the complete picture.

8 ÷ 1 = 8

8 ÷ 2 = 4

8 ÷ 4 = 2

8 ÷ 8 = 1

Thus, the factors of 8 are 1, 2, 4, and 8.

How to Calculate the Factors of 8?

There are two methods to find the factors of 8 as follows:

1. Factors of 8 By Division Method
2. Factors of 8 By Prime Factorization Method

As we know, in prime factorization, we express the number 8 as the product of its prime factors. Similarly, in the division method, we look for numbers that divide the number 8 exactly without leaving any remainder.

Factors of 8 By Division Method

Since 8 is a composite number, it will have more than two factors. Let us calculate all the factors of the 8 by the division method. The first step is to divide 8 with the smallest prime factor, which is 2, followed by the others.

8 ÷1 = 8

8 ÷ 2 = 4

8 ÷ 4 = 2

8 ÷ 8 = 1

As we have seen, the division method shows that 8 is exactly divisible by four numbers that are 1, 2, 4, and 8. Therefore, the total factors of 8 by division are 1, 2, 4, and 8. Have you noticed that all the factors are equal or less than 8? 

Factors of 8 By Prime Factorization

You can also find the factors of 8 by prime factorization. It is, actually, the upside-down division method 

The factors of 8 by the prime factorization method are 1, 2, 4, and 8. Here, 2 is the only prime factor of 8. 

Factors of -8

To find the factors of -8, we will follow the same process as we have done above. These factors give the product (-8) when multiplied.

-1 x  8 = -8

 1 x -8 = -8

-2 x  4 = -8

 2 x -4 = -8

From the above process, we can make pair factors of -8 as follows:

(-1 x 8), (1 x -8), (-2 x 4) and (2 x -4).

With the help of the above illustrations, let’s explore the following factors:

Factors of 9:

(1,3,9)

Factors of 10:

(1, 2, 5, 10)

Factors of 15:

(1, 3, 5, 15)

Factors of 180:

(1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180)

Factors of 20:

(1, 2, 4, 5, 10, 20)

Factors of 8 in Pairs

Every number has factors except 0, and we can make a set of positive and negative factors. To find the positive factors of 8 in pairs, we will multiply the two numbers in a pair to get the resultant.

Positive Factors of 8 in Pairs

1 × 8 = 8 (1, 8) is a pair 

2 × 4 = 8 (2, 4) is a pair 

Therefore, (8, 1) and (2, 4) are the positive factors of 8 in pairs.

Negative Factors of 8 in Pairs

-1 × -8 = 8 (1, 8) is a pair 

-2 × -4 = 8 (2, 4) is a pair 

Therefore, (-8, -1) and (-2, -4) are the positive factors of 8 in pairs.

Notables:

• Factors 8 are 1, 2, 4, and 8.
• 1 is a universal and primary factor of all numbers except zero (0).
• The positive factors of 8 in pairs are (2, 4) and (1, 8).
• The negative factors of 8 in pairs are (-2, -4) and (-1, -8).
• 2 is the only prime factor of 8.

Solved Examples

Example 1:

Calculate the common factors of 8 and 84.

Solution:

There are 11 factors of 8: 1, 2, 4, 8

All factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

Therefore, 70 and 84 have a common factor of 1, 2, and 4.

Example 2:

Calculate the common factors of 8 and 24.

Solution:

The factors of 8 are 1, 2, 4, 8

Find the prime factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

As 71 is a prime number, the common factor of 8 and 24 is 1, 2, 4, and 8 only.

Example 3:

Calculate the common factor of 47 and 8.

Solution:

All Factors of 47= 1 and 47.

Find the prime factors of 8=1, 2, 4, and 8.

As a result, 38 and 8 have 1, and 2 common factors.

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