Factors of 8

The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8. Hence, the highest factor is 8 which divides itself. If we add all the factors, then the sum will be equal to 15. 

The pair factors of 8 are (1, 8) and (2, 4). These pair factors when multiplied together result in the original number. 8 is also a perfect cube. We can determine the factors of 8 by the division method and prime factorisation method.

What are the Factors of 8?

A number or an integer that divides 8 exactly without leaving a remainder, then the number is a factor of 8. As the number 8 is an even composite number, it has more than two factors. Thus, the factors of 8 are 1, 2, 4 and 8.

Pair Factors of 8

A pair of numbers, which are multiplied together resulting in an original number 8 is called the pair factors of 8. As discussed above, the pair factors of 8 can be positive or negative. The positive and negative pair factors of 8 are given below:

Positive Pair Factors of 8:

Negative Pair Factors of 8:

How to Find Factors of 8?

8 is a whole number that is also an even number. Since it is a single-digit number, therefore, it is much easier to find the factors of 8.

There are two methods to find the factors of 8:

• Division method
• Prime factorisation method

Factors of 8 by Division Method

The factors of 8 can be found using the division method. In the division method, we need to find the integers which divide 8 exactly without leaving a remainder, and those integers are considered as the factors of 8. Now, let us find the factors of 8 using the division method.

• 8/1 = 8 (Factor is 1 and Remainder is 0)
• 8/2 = 4 (Factor is 2 and Remainder is 0)
• 8/4 = 2 (Factor is 4 and Remainder is 0)
• 8/8 = 1 (Factor is 8 and Remainder is 0)

If we divide 8 by any numbers other than 1, 2, 8 and 8, it leaves a remainder. Hence, the factors of 8 are 1, 2, 4 and 8.

Prime Factorization of 8

The prime factorization of 8 is the process of writing the number as the product of its prime factors. Now, let us discuss the process of finding the prime factors of 8.

• Divide 8 by the smallest prime number, i.e. 2, i.e., 8/2 = 4.
• Divide 4 by the smallest possible prime number, i.e., 4/2 = 2.
• 2 is itself a prime number and is divisible by 2.
• Therefore, the prime factorization of 8 is 2 × 2 × 2 or 2³.

Video Lesson on Prime Factors

Another method to find the prime factors of 8 is the factor tree method.

Factor Tree

Hence, the number of unique prime factors of 8 is one. The prime factorisation of the whole number 8 is 2³. The exponent in the prime factorisation is 3. When you add the number 1 with the exponent, i.e., 3 +1 = 4. Therefore, the number 8 has 4 factors.

Facts – Factors of 8

• Factors of 8: 1, 2, 4 and 8
• Prime factorisation: 2 × 2 × 2
• Prime factor of 8: 2
• Pair factors: (1, 8) and (2, 4)
• Sum of factors of 8: 15

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Solved Examples on Factors of 8

Example 1:

Find the common factors of 8 and 5.

Solution:

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

The factors of 5 are 1 and 5.

As 5 is a prime number, the common factor of 8 and 5 is 1.

Example 2:

Find the common factors of 8 and 9.

Solution:

Factors of 8 = 1, 2, 4 and 8.

Factors of 9 = 1, 3, and 9.

Hence, the common factor of 8 and 9 is 1.

Example 3:

Find the common factors of 8 and 4.

Solution:

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

The factors of 4 are 1, 2 and 4.

Hence, the common factors of 8 and 4 are 1, 2, and 4.

Practise Questions on Factors of 8

1. What is the lowest factor of 8?
2. Is there any odd number that is a factor of 8?
3. How many even numbers are the factors of 8?

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