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Factors of 8: Prime Factorization, Methods, Tree, and Examples
Factors of 8 are a set of numbers that evenly divide 8, leaving no remainder. The remainder must be zero. Only then will that whole number will be considered as a factor of 8.
Figure 1 – All possible Factors of 8
What Are the Factors of 8?
Factors of 8 are 1, 2, 4, and 8; there are eight total factors of 8. Four represent positive factors, and the other four represent negative factors.Whole numbers added to this list of factors are the numbers that completely divide 8 leaving the remainder zero. A number having more than 2 factors is known as a composite number. 8 is a composite number.How To Calculate the Factors of 8?
You can calculate the factors of 8 by two different methods: Division Method and Multiplication Method.Now let’s understand how to calculate the factors of a number using the division method. This method takes more time as you have to divide the given number by different numbers but it is not difficult.To find factors of 8, start dividing it by different numbers and check whether the remainder is zero or not. If the remainder is zero, note those numbers under the list of factors of 8. If the remainder is a non-zero drop down the number and divides the given number by the next possible number. Always start dividing from the smallest number which is one. 1 is a factor of every number because 1 divides every number completely. As a result of the above discussion 1 is a factor of 8.\[\dfrac{8}{1} = 8 \]8 is an even number, so it will be divisible by 2.\[\dfrac{8}{2} = 4 \]2 divides 8 evenly and the remainder is also zero, so 2 is a factor of 8.\[\dfrac{24}{3} = 8 \]Divide 8 by 3\[\dfrac{8}{3} = 2.66 \]When we divide 8 by 3, it results in 2.66, which is a decimal number, and the remainder is 2. Two is a non-zero number, this means 3 is not a factor of 8.Divide 8 by 4\[\dfrac{8}{4} = 2 \]The remainder is zero, so 4 is a factor of 8.Divide 8 by 6 \[\dfrac{8}{6} = 1.33 \]When we divide 8 by 6, it results in 1.33, which is a decimal number, and the remainder is 2, which is a non-zero number as a result 6 is also not a factor of 8.Now divide 8 by 8 \[\dfrac{8}{8} = 1 \]Every number divides itself fully with the remainder zero. Every number is a factor in itself.From the above calculations, we conclude that the factors of 8 are :Factors of 8 = 1, 2, 4, 8Negative factors of 8 are:Negative factors of 8 = -1, -2, -4, -8Fun Facts
- 1 is a factor of every number.
- The greatest factor in the factor list is equal to the number itself.
- 2 is a factor of every even number.
- Any number that is greater than 0 and its ending number is 0 has 2, 5, and 10 as its factors.
- Factors can never be in fractional or decimal form.
- Factorization is a common way to solve algebraic equations.
Factors of 8 by Prime Factorization
Prime Factorization is a method of multiplying factors of a number that are prime. The product of such multiplication will be equal to the original number. Prime factors are the factors of a number that are divisible by 1 or the number itself. The algorithm for finding the prime factorization of a number is to start dividing the number by its prime factors. You always have to start dividing by the smallest prime factor.Factors of 8 = 1, 2, 4, 8 By the above list of factors, we pick the prime factors. 1 is not a prime number. We have only the prime number 2. Start by dividing 8 by 2.\[\frac {8}{2}= 4\]Divide it by 2 because 4 is divisible by 2.\[\frac {4}{2}= 2\]Again, divide it by 2.\[\frac {2}{2}= 1\]Now write it in the form of a table.The Prime Factorization of 8 is shown below in figure 1:
Figure 2 – Prime Factorization of 8
2 x 2 x 2 = 8
The above equation can also be written as:\[ 2^3 = 8 \]Factor Tree of 8
The factor tree is a way of representing the prime factorization in the form of a tree. The factor tree contains the number at the top that is being divided by its prime factors. After the division number splits into the divisors and the quotients.Initially, we will divide 8 by its prime factor 2. \[\frac {8}{2}= 4 \]8 splits into the 2 (divisor) and 4 (quotient). Now 4 will be divided by 2.\[\frac {4}{2}= 2\]4 will be branched into 2 (divisor) and 2(quotient).The factor tree of 8 is shown below in figure 2:
Figure 3 – Factor Tree of 8
Prime Factorization
2 x 2 x 2 = 8
By observing the above equation, we concluded that 8 is a perfect square.Factors of 8 in Pairs
Factor pairs are a set of factors that produce the original number when multiplied.We can find factors of 8 by the following multiplication:1 x 8 = 8
2 x 4 = 8
The factor pairs of 8 can be written as:(1, 8)(2, 4)A number can have both positive and negative factor pairs. 8 has 2 positive factor pairs.We can find negative factors of 8 by the following multiplication:-1 x -8 = 8
-2 x -4 = 8
The negative factor pair of 8 are:(-1, -8)
(-2, -4)
Factors of 8 Solved Examples
Let’s solve some examples related to the factors of 8 for a better understanding.Example 1
List the factors of 8 in descending order, calculate the sum S1 of the middle two factors, and then calculate the product of the first and last factors. Label it as P1. Prove that S1 is greater than P1Solution
The factors of number 8 are:Factors of 8 = 1, 2, 4, 8 The factors of number 8 in descending order:Factors of 8 in descending order = 8, 4, 2, 1 As the two middle factors are 4 and 2, their sum is:Sum S1:4+ 2 = 6
As the first and last factor is 8 and 1, their product is:Product P1:1 x 8 = 8
From the above calculations, we conclude that S1 is not greater than P1.