Education Content Expert
Factors of 8 are the list of integers that divide 8 exactly without leaving any remainder. There are 4 factors of 8 which are 1, 2, 4, and 8. 1 is the smallest factor of 8 while the biggest factor of 8 is 8 which divides itself. The sum of all the factors of 8 is 15. The two pair factors of 8 are (1, 8) and (2, 4). The prime factorization of 8 is 2 x 2 x 2 or 23. 2 is the only prime number that divides 8 completely. 8 is also a perfect cube. The factors of 8 can be determined by division as well as prime factorization.
| Table of Content |
Key Terms: Factors of 8, Prime Factorization, Division, Prime Numbers Multiplication, Factors, Pair Factors, Prime Factors
What are Factors of 8?
[Click Here for Sample Questions]
Factors of 8 refer to the numbers or integers that divide 8 exactly. 8 is an even composite number indicating that it has more than two factors. There are total 4 factors of 8. 1, 2, 4, and 8 are the factors of 8.
Factors of 8 = 1, 2, 4, 8
Read More:
| Relevant Concepts | ||
|---|---|---|
| Factors of 12 | Factors of 48 | Factors of 28 |
| Factors of 24 | Factors of 25 | Factors of 16 |
Factors of 8 in Pairs
[Click Here for Sample Questions]
If a pair of numbers on multiplication with each other results in the original number 8, then that set of numbers is called the pair factors of 8.
Example: 1 × 8 = 8, thus, (1, 8) is a pair factor of 8.
Pair Factors of 8 can be positive or negative. The positive and negative pair factors of 8 are as follows:
Positive Pair Factors of 8
The positive pair factors of 8 are (1, 8) and (2, 4).
| Positive Factors of 8 | Positive Pair Factors of 8 |
|---|---|
| 1 × 8 | (1, 8) |
| 2 × 4 | (2, 4) |
Negative Pair Factors of 8
The negative pair factors of 8 are (-1, -8) and (-2, -4).
| Negative Factors of 8 | Negative Pair Factors of 8 |
|---|---|
| -1 × -8 | (-1, -8) |
| -2 × -4 | (-2, -4) |
Factor Tree of 8
[Click Here for Sample Questions]
2 is the only prime factor of 8. The prime factors of 8 can be represented in the form of a factor tree as follows:
Factor Tree of 8
How to Calculate Factors of 8?
[Click Here for Sample Questions]
8 is an even whole number. 8 is a single-digit number which makes it easy for us to find the factors of 8. We can find out the factors of 8 with the help of two methods:
- Division Method
- Prime Factorisation Method
Both of the methods would result in the same factors which are 1, 2, 4, and 8.
Factors of 8 by Division Method
[Click Here for Sample Questions]
Factors of 8 can be found with the help of the division method. In order to use the division method to calculate the factors of 8, we need to check the numbers whether they divide 8 exactly without leaving a remainder or not. The factors of 8 using the division method are as follows:
- 8 ÷ 1 = 8 (Factor = 1; Remainder = 0)
- 8 ÷ 2 = 4 (Factor = 2; Remainder = 0)
- 8 ÷ 4 = 2 (Factor = 4; Remainder = 0)
- 8 ÷ 8 = 1 (Factor = 8; Remainder = 0)
Now, if we divide any other number than 1, 2, 8 and 8, it leaves a remainder. Thus, the factors of 8 are 1, 2, 4, and 8.
Prime Factorization of 8
[Click Here for Sample Questions]
Prime factorization of 8 refers to the expression of the number 8 as the product of its prime factors. Here is how we can get the prime factors of 8:
- In the first step, divide 8 by the smallest prime number which is 2. 8 ÷ 2 = 4.
- Now, divide 4 by the smallest prime number again, i.e., 4 ÷ 2 = 2.
- We know that 2 is itself a prime number and is divisible by 2.
- Eventually we get 1 at the end and we cannot proceed further.
- Thus, the prime factorization of 8 is 2 × 2 × 2 or 23 with 2 as the only prime factor of 8.
Prime Factorization of 8
Solved Examples on Factors of 8
[Click Here for Sample Questions]
Example 1: What are the common factors of 8 and 9?
Solution: The factors of 8 and 9 are
- Factors of 8: 1, 2, 4, and 8.
- Factors of 9: 1, 3, and 9.
Thus, there is only one common factor of 8 and 9 which is 1.
Example 2: What are the common factors of 8 and 4?
Solution: All the factors of 8 and 4 are
- Factors of 8: 1, 2, 4, and 8.
- Factors of 4: 1, 2, and 4.
Thus, there are three common factors of 4 and 8 which are 1, 2, and 4.
Read More:
| Related Topics | ||
|---|---|---|
| LCM Formula | Relation Between HCF and LCM | Properties of LCM and HCF |
| LCM of Two Numbers | HCF | Greatest Common Divisor |
Things to Remember
- Factors of 8 are the numbers that divide 8 exactly with zero as the remainder.
- Factors of 8 are 1, 2, 4, and 8.
- Factors of 8 in pairs are the numbers that when multiplied together give the original number.
- The factors of 8 in pairs are (1, 8), and (2, 4).
- The prime factorization of 8 is 2 x 2 x 2 or 23.
- 2 is the only prime factor of 8.
Sample Questions
Ques. Check which numbers from the given list are not factors of 8. The list of numbers is 1, 2, 3, 4, 5, 6, 7, and 8. (3 Marks)
Ans. We know that if a number divides 8 completely without leaving any remainder, then it is a factor of 8. So going through this criteria, we can say that
- 1, 2, 4, and 8 are the factors of 8 as they do not leave any remainder on dividing 8 by them.
- When we divide 8 by 3, 5, 6, and 7, the remainder is left which means 3, 5, 6, and 7 are not the factors of 8.
Ques. Himanshi was asked to find the common factors of 8 and 18. What will be her answer? (2 Marks)
Ans. First, we need to write down all the factors of 8 and 18.
- Factors of 8: 1, 2, 4, and 8
- Factors of 18: 1, 2, 3, 6, 9, and 18.
Thus, the common factors of 8 and 18 are 1 and 2.
Ques. What are the common factors of 8 and 5? (2 Marks)
Ans. Write down the factors of 8 and 5, we get
- Factors of 8: 1, 2, 4, and 8
- Factors of 5: 1, and 5
Thus, the only common factor of 8 and 5 is 1.
Ques. What are the factors of 8? (2 Marks)
Ans. Factors of 8 are the numbers that divide 8 completely leaving zero as the remainder. The factors of 8 are as follows:
- 8 ÷ 1 = 8
- 8 ÷ 2 = 4
- 8 ÷ 4 = 2
- 8 ÷ 8 = 1
Thus, there are four factors of 8 which are 1, 2, 4, and 8.
Ques. What is the prime factorization of the number 8? (2 Marks)
Ans. 8 is a composite number which means that it has prime factors. The prime factorization of 8 is 2 × 2 × 2 or it can also be written as 23. Here, 2 is the only prime factor of 8.
Ques. Find out the sum of all factors of 8. (2 Marks)
Ans. We know that 8 has four factors which are 1, 2, 4, and 8.
On adding all these factors of 8, we get
1+ 2 + 4 + 8 = 15
Thus, the sum of all factors of 8 is 15.
Ques. List the positive and negative pair factors of 8. (2 Marks)
Ans. Pair factors of 8 are the set of numbers that give the number 8 on multiplication with each other. They can be positive as well as negative as the negative pair factor would also result in the positive number 8 only.
The positive pair factors of 8 are (1, 8) and (2, 4) while the negative pair factors of 8 are (-2, -4) and (-8, -1).
Ques. Name the greatest common factor of 8 and 7. (2 Marks)
Ans. 7 is a prime number which means that it has no other factors than 1 and the number itself. Also, 7 is also not a factor of 8. It means that the only common factor of 7 and 8 is 1, thus, 1 is the greatest common factor of 8 and 7.
Ques. Check whether 2 is a factor of 8 or not. (2 Marks)
Ans. To check whether 2 is a factor of 8 or not, we need to divide 8 by 2 and see if the remainder is zero.
8 ÷ 2 = 4
Thus, yes, 2 is a factor of 8 as it leaves a quotient of 4 and remainder 0, which means it divides 8 completely.
Ques. Name the greatest common factor of 8 and 6. (2 Marks)
Ans. The factors of 8 and 6 are
- Factors of 8: 1, 2, 4, and 8
- Factors of 6: 1, 2. 3 and 6
There are two common factors of 8 and 6 which are 1 and 2. Thus, the Greatest Common Factor (GCF) of 8 and 6 is 2.
Read More:
Comments