Factors

# Factors of 8 | Prime Factorization of 8 | Factor Tree of 8

Written by Prerit Jain

Updated on: 08 Jun 2023

Contents

### Factors of 8 | Prime Factorization of 8 | Factor Tree of 8

## Factors of 8

Factors of 8 | Factor Pairs of 8 | Prime factors of 8 |

1, 2, 4, 8 | (1,8) (2,4) (4,2) | 2 x 2 x 2 |

Calculate Factors of

**The Factors are**

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## What are the factors of 8

Factors of a given number are the numbers that can divide the given number without any remainder and any decimal points in the quotient. For example, the factors of 8 are 1, 2, 4, and 8 because these numbers can divide by 8 without any remainder.

Factors are an important concept in Mathematics and are used in many different ways. For instance, factors can be used to find the greatest common factor (GCF) of two numbers, which is the largest number that both numbers can be divided by. For example, the GCF of 12 and 16 is 4, because 4 is the largest number that both 12 and 16 can be divided by.

Factors can also be used to determine whether a number is prime or composite. A prime number is a number that has only two factors: 1 and itself. For example, the first six prime numbers are 2, 3, 5, 7, 11, and 13. A composite number, on the other hand, is a number that has more than two factors. For example, 8 is a composite number because it has four factors: 1, 2, 4, and 8.

## How to Find Factors of 8

To find the factors of 8, you can use one of the following methods:

- Factor of 8 using the Multiplication Method
- Factors of 8 using the Division Method
- Prime Factorization of 8
- Factor tree of 8

## Factors of 8 using the Multiplication Method

To find the factors of 8 using the multiplication method, you can follow these steps:

- Start by writing down the number 8.
- Write down the factors of 8 in pairs, such that the product of each pair is equal to 8. For example, you can write down the pairs (1, 8) and (2, 4).
- Determine the factors of 8 by multiplying the numbers in each pair. The factors of 8 are 1, 2, 4, and 8.

This method involves writing down the factors of 8 in pairs and then finding the factors by multiplying the numbers in each pair. For example, you can write down the pairs (1, 8) and (2, 4), and then find the factors of 8 by multiplying the numbers in each pair to get 1, 2, 4, and 8.

## Factors of 8 through Division Method

To find the factors of 8 using the division method, you can follow the steps given below:

- Write down the number 8.
- Divide 8 by increasing integers until you find all of the factors. For example, you can divide 8 by 2, then 3, then 4, and so on.
- Write down the integers that produce a whole number result when divided by 8. Thus, the factors of 8 are 1, 2, 4, and 8.

This method involves dividing 8 by increasing integers until you find all of the factors. You can start dividing 8 by 2, then 3, then 4, and so on. The factors of 8 are the integers that produce a whole number result when divided into 8, which are 1, 2, 4, and 8.

## Prime Factorization of 8

Calculate Prime Factors of

The Prime Factors of 8 =

2 x

2 x

2

The prime factorization of 8 is the expression of 8 as the product of its prime factors. The prime factorization of 8 is 2 x 2 x 2 because 8 can be expressed as the product of three 2s (2 x 2 x 2 = 8).

To find the prime factorization of a number, you can express the number as the product of its prime factors. For example, the prime factorization of 15 is 3 x 5, because 15 can be expressed as the product of the prime numbers 3 and 5 (3 x 5 = 15).

The prime factorization of a number is written as the product of its prime factors. For example, **the prime factorization of 8 is written as 2 x 2 x 2, or 2^3.**

## Factor tree of 8

To create a factor tree for 8, you can follow these steps:

- Write down the number 8 and draw a line beneath it.
- Determine the smallest prime factor of 8. In this case, it is 2. Write this factor to the left of the line and draw another line beneath it.
- Divide 8 by the factor that you just found (2). Write the result (4) to the right of the line and draw another line beneath it.
- Repeat this process until you reach a prime number. In this case, 4 is not a prime number, so you will need to divide it by another factor. The smallest prime factor of 4 is 2, so you can write this factor to the left of the line and draw another line beneath it. 4 divided by 2 is 2, so you can write 2 to the right of the line.
- At this point, you have reached a prime number, so you can stop the process.
**The prime factorization of 8 is 2 x 2, or 2^2.**

## Factor Pairs of 8

Calculate Pair Factors of

1 x 8=8

2 x 4=8

4 x 2=8

So Pair Factors of 8 are

(1,8)

(2,4)

(4,2)

A factor pair is a combination of two numbers that can produce the given number when multiplied together. To find the factor pairs of 8, you can follow these steps:

- Write down the number 8.
- Write down the factors of 8 in pairs, such that the product of each pair is equal to 8. For example, you can write down the pairs (1, 8) and (2, 4).
- Determine the factor pairs of 8 by multiplying the numbers in each pair. In this case, the factor pairs of 8 are (1, 8) and (2, 4).

Here is what the process would look like:

- Write down the number 8.
- Write down the factor pairs: (1, 8), (2, 4).
- Determine the factor pairs: (1, 8), (2, 4).

## More Factors

## Factors of 8 – Quick Recap

**Factors of 8:**1, 2, 4, and 8.**Negative Factors of 8:**(-1, -8) and (-2, -4).**Prime Factors of 8:**2 × 2 × 2**Prime Factorization of 8:**2 × 2 × 2

## Factors of 8 – Fun Facts

- The factors of 8 are the numbers that can be multiplied together to produce 8. The factors of 8 are 1, 2, 4, and 8.
- The number 8 is a perfect cube, which means that it can be written as the product of three equal integers. In this case, the three equal integers are 2 x 2 x 2, or 2^3.
- The number 8 is also a perfect power of 2. This means that it can be written as the product of two equal integers, with one of the integers being 2. In this case, the two equal integers are 2 x 2, or 2^2.
- The number 8 is considered to be a lucky number in some cultures, as it is considered to be a symbol of abundance and prosperity.

**Also Check**: Multiples, Square Root, and LCM

## Solved Examples of Factor of 8

**Q.1: If a number is divisible by 8, what is the greatest digit in the number? Solution**: The greatest digit will always be 8.

**Q.2: If a number divided by 8 has a remainder of 4, what is the number? Solution**: The number is 36 (36 ÷ 8 = 4 with 4 as the remainder).

**Q.3: If two numbers have a greatest common factor of 8, what is their lowest common multiple? ****Solution**: Their lowest common multiple would be 8² or 64.

**Q.4: If one side of a triangle measures 16 cm and another side measures 10 cm, what would its area be if it were a right triangle with an angle of 60 degrees? **

**Solution**: Its area would be 80 cm² (16 x 10 / 2).

**Q.5: How many integers between 1 and 100 are multiples of eight? **

**Solution**: There are 13 integers between 1 and 100 that are multiples of eight; they include 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96.

**Q.6: What is the mean of all integers between 1 and 100 which are divisible by 8? ****Solution**: The mean would be 52 (summing all numbers up to 96 divided by 12).

**Q.7: If eleven people have 11 items each and each item must have an equal factor of 16 what would need to be added so that each person has equivalent items?Solution**: In this case, you would need to add 3 items so that each person has equivalent items (11 x 16=176 + 3 = 179).

**8. If a square measures eight units wide and eight units high, find its perimeter. Solution**: The perimeter for this square would be 32 units (2 x 8 + 2 x 8 = 32)

**9. Find the smallest multiple of twelve that contains at least one prime factor no greater than 17.**

**Solution**: 204 is the smallest multiple that contains at least one prime factor no greater than 17; its prime factors are 4×17 = 68).

**10. Find four integers whose product results in 1776 when multiplied together where none exceed 17 but still have an equal factor of 17 within each integer?Solution**: 4, 9, 11, 16 as these four multiplied together to give 1776 which also includes an equal factor of seventeen within each integer (4 x 9 x 11 x 16 = 1776; 4¹×9¹×11¹×16¹=17⁴)

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## Frequently Asked Questions on Factors of 8

**What is a factor of 8? **

A factor of 8 is any number that can be divided evenly into 8. Factors of 8 include 1, 2, 4, and 8.

**How many factors do 8 have?**

Eight has four different factors; they include 1, 2, 4, and 8.

**What is the greatest common factor (GCF) of 8? **

The greatest common factor (GCF) of 8 is 4; it’s the largest number that both divide into without a remainder.

**Is 1 a factor of 8? **

Yes, 1 is a factor of 8 as it can be divided evenly into eight with no remainder.

**Is the number 9 a multiple of 8? **

No, 9 is not a multiple of eight as it cannot be divided evenly into eight with no remainder.

**What are some multiples of eight?**

Multiples of eight include 16, 24, 32, 40, etc.; any number that can be divided evenly by eight with no remainder is considered to be a multiple of eight.

**What two numbers have an even product when multiplied together whose sum also equals eight?**

Two numbers that have an even product when multiplied together whose sum is also equal to eight are 1 and 7 (1×7 = 7; 1+7 =8).

**Is 3 prime or composite in relation to the number 8?**

3 is prime in relation to the number 8 as both cannot be divided by others other than themselves without leaving a remainder (non-prime numbers).

**Is 11 divisible by any powers greater than three in relation to the number 8?**

No, 11 cannot be divisible by any powers greater than three in relation to the number 8; it cannot be divided into any power up to eleven without leaving a remainder so 11 would remain non-divisible from power three onwards in relation to the number eight.

**How do you find all possible permutations or combinations for the factors multiplying together to equal eighteen but none exceeding seven?**

All possible permutations or combinations for factors multiplying together to equal eighteen but none exceeding seven would include 6×2=12 and 5×3=15 as these two equations fit within this criteria (6×2 = 12 and 5×3 = 15; neither exceeds 7).

Written by by

Prerit Jain