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Factors of 88: Prime Factorization, Methods, Tree, and Examples

Factors of a number are the natural numbers that fully divide the given number—leaving the remainder zero. Factors are numbers that can not be written in fractional form. Factors of a number are also known as its divisors.

The number 88 is even composite, which means more than two whole numbers are factors of 88. We can find factors of 88 by the division method and multiplication method, also known as the factor pair method. In this article, we will learn about factors of 88, techniques to find them, factor tree, and examples.

Figure 1 – All possible Factors of 88

## What Are the Factors of 88?

Factors of 88 are 1, 2, 4, 8, 11, 22, 44, and 88; all of these natural numbers divide 88 fully. The numbers listed above fulfill the requirements of being a factors list. 88 is a composite number, so there are sixteen total factors of 88. Eight are positive factors and the remaining eight are negative factors.

## How To Calculate the Factors of 88?

You can calculate the factors of 88 by two standard methods: division and multiplication method. We will discuss division methods in this article. There are two types of factors of a number: positive and negative. They differ by a minus sign. To find the factors of 88, draw a number line starting from 1 and ending on 88. We have to consider the contributing numbers (factors) in between them. Factors of 88 by division method: It’s a fact that the number one is a factor of every whole number because every number is completely divided by 1, leaving the remainder zero. \[ \frac{88}{1} = 88 \] \[ \frac{88}{-1} = -88 \] The number 1 and -1 are factors of 88. 88 is not even, so it will be evenly divided by 2. \[ \frac{88}{2} = 44 \] \[ \frac{88}{-2} = -44 \] The numbers 2 and -2 both are the factors of 88. Let’s divide 88 by 3: \[ \frac{88}{3} = 29.33 \] \[ \frac{88}{-3} = -29.33 \] When we divide 88 by 3 or -3, the quotient is not a whole number. The remainder is not zero. Condition of factors is not satisfied. Hence, 3 is not a factor of 88. Divide 88 by 4: \[ \frac{88}{4} = 22 \] \[ \frac{88}{-4} = -22 \] When 88 is divided by 4, the number is evenly divided, and the remainder is 0. The condition of factors is fully satisfied, and as a result, 4 and -4 are the factors of 88. Divide 88 by 6: \[ \frac{88}{6} = 14.67 \] \[ \frac{88}{-6} = -14.67 \] When we divide 88 by 6 or -6, the condition of factors is not satisfied. A remainder is a non-zero number. By the above calculation, we will not consider six as a factor of 88. Divide 88 by 11: \[ \frac{88}{11} = 8 \] \[ \frac{88}{-11} = -8 \] When 88 is divided by 11 or -11, the remainder in both cases is zero. Condition is satisfied, so 11 and -11 are the factors of 88. Divide 88 by 22: \[ \frac{88}{22} = 4 \] \[ \frac{88}{-22} = -4 \] When 88 is divided by 22, condition of factors is not satisfied for both negative and positive 22. As a result of the above calculation, 22 and -22 are the factors of 88. Divide 88 by 44: \[ \frac{88}{44} = 2 \] \[ \frac{88}{-44} = -2 \] When 88 is divided by 44, the remainder is zero. As a result, 44 and -44 are the factors of 88. Every whole number is a factor in itself. As every whole number divides itself evenly and the remainder is always zero, 88 and -88 are the factors of 88. \[ \frac{88}{88} = 1 \] \[ \frac{88}{-88} = -1 \]

List of positive factors of 88 = 1, 2, 4, 8, 11, 22, 44, and 88.

List of negative factors of 88 = -1, -2, -4, -8, -11, -22, -44, and -88.

## Factors of 88 by Prime Factorization

The mathematical technique used to write the given whole number as the product of its prime factors is known as Prime Factorization. Prime factorization is a mathematical process used to generate a given number by multiplying the prime factors of that number. Only composite numbers can be represented using this technique. Note that the number one is not a prime number. Finding prime factorization by simple division method: The first step is to list the prime factors of 88. List of prime factors of 88: 2 and 11. To begin with, divide the number 88 by the smallest prime factor. The smallest prime factor in the list above is 2. \[ \frac{88}{2} = 44 \] 44 is the quotient, and it is again divisible by 2. \[ \frac{44}{2} = 22 \] The quotient is 22. The number 22 is divisible by 2. \[ \frac{22}{2} = 11 \] The quotient is 11. The number 11 is not divisible by 2, so we will divide it by the next prime factor, 11. \[ \frac{11}{11} = 1 \] The quotient is 1. The division is terminated. The Prime Factorization of 88 is shown below in figure 1:

Figure 2 – Prime Factorization of 88

## Factor Tree of 88

The factor tree is a pictorial way of representing the factors of a whole number, mostly the prime factors. A factor tree is similar to a tree. You can also consider it as a number tree. Now we will learn how to construct a factor tree. Write the number for which factor tree is being constructed at the top. Split that whole number using two branches. Fill these branches with the help of factors of the number. Repeat the division process until each branch ends up with the prime factors. The factor tree of 88 is shown below in figure 2:

The prime factorization of 88 can be written as:

Figure 3 – Factor Tree of 88

Prime Factorization of 88: 2 x 2 x 2 x 11

## Factors of 88 in Pairs

Writing a pair of factors of 88, when multiplied, gives a whole particular number equal to the given number. Factoring is a famous technique used to solve simple and complex level algebraic equations. When we multiply two different numbers to get a specific product, the whole numbers being multiplied are called the factors of that product. A real-life example always makes things easier to understand. For example, they divide crayons among students, arrange the paper in files, distribute pizza slices among kids, etc. We can find the factor pairs by the simple multiplication method. Factor pairs can be positive and negative, but they can’t be in fractional or decimal form. Finding factor pairs using the multiplication method:

1 x 88 = 88

2 x 44 = 88

The positive factor pairs of 88 are the following:

(1, 88)

(2, 44)

Finding negative factors of 88:

-1 x -88 = 88

-2 x -44 = 88

The negative factor pairs of 88 are the following:

(-1, -88)

(-2, -44)

## Factors of 88 Solved Examples

### Example 1

Sam has 88 red roses and 24 white roses. He wants to make bouquets with the same number of each color roses in each bouquet. What is the greatest number of bouquets he can make?

### Solution

The given condition is: 88 red roses and 24 white roses The same number of each color roses in each bouquet. The Greatest Common Factor of two numbers is the greatest number from the list of factors of both numbers that ultimately divides both numbers. List of factors of 88: 1, 2, 4, 8, 11, 22, 44, and 88. List of factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24. Find the greatest common number from the lists of factors above. The number 8 is the greatest common factor between 88 and 24.

Sam will be able to make eight bouquets.

Each bouquet will have 11 red roses and three white roses.

11 x 8 = 88

3 x 8 = 24

### Example 2

Find the sum S1 of all odd factors of 88 and divide it by the sum S2 of the even factors of 88.

### Solution

List of factors of 88: 1, 2, 4, 8, 11, 22, 44, and 88. List of even factors of 88: 2, 4, 8, 22, 44, and 88. List of odd factors of 88: 1 and 11. Finding the sum of all even factors of 88:

Sum S1: 2 + 4 + 8 + 22 + 44 + 88 = 168

Finding the sum of all odd factors of 88:

Sum S2: 1 + 11 = 12

\[ \frac{168}{12} = 14 \] Dividing the sum of all even factors of 88 by the sum of all odd factors of 88, we get 14. Images/mathematical drawings are created with GeoGebra.