# Factors of 119: Prime Factorization, Methods, Tree, and Examples

Factors of 119 are the group of natural numbers, that when multiplied by one another, produce 119 as the product. The numbers that are completely divisible by 119 are also referred to as factors of 119.

Figure 1 – All possible Factors of 119

Factors of a given number are termed as its divisors such that these divisors are believed to be a set of natural numbers that when divided by the given number leave zero as its remainder. In this article, we will be discussing various techniques and methods used to find the factors of 119, the prime factorization of 119, its factor tree representation, and the factor pairs of 119.

## What Are the Factors of 119?

The factors of 119 are 1, 7, 17, and 119. All of them are factors of 119 as they completely divide 119 and leave 0 as a remainder. The factors of any given number can also be defined as the product of two natural numbers such that the product is equivalent to the given number. Hence, the two natural numbers are the factors of the given number. Similarly in the case of factors of 119, the product of 7 and 17 gives 119 as the result therefore they are the factors of 119.

## How To Calculate the Factors of 119?

You can calculate the factors of number 119, by checking whether the given number i.e. 119 is divisible by the specified natural numbers or not. If yes, such that the remainder of the division appears to be zero then the suggested number is considered to be the factor of 119. The following steps must be followed to find the factors of 119. Starting with the smallest natural number i.e. ‘1’, which is also commonly known as the universal factor. Divide the number 119 by 1. Now, check the remainder. Is it zero? $\dfrac{119}{1} = 119$ Yes, it is. Hence, it is clear that 1 is a factor of the number 119. Similarly, when dividing 119 by 2, the remainder is not equal to zero. Therefore, it is proved that 2 is not the factor of 119. Now, divide 119 by 7 and 17. $\dfrac{119}{7} = 17$ $\dfrac{119}{17} = 7$ Therefore, it is concluded that 7 and 17 are the factors of 119. Both of them are prime numbers. The number 119 is a composite number having four factors. Composite numbers are numbers with more than two factors, unlike prime numbers. The factors of 119 are given as: $\dfrac{119}{1} = 119$ $\dfrac{119}{7} = 17$ $\dfrac{119}{17} = 7$ $\dfrac{119}{119} = 1$ The negative factors of any given number are nothing but the additive inverse of the factors of that number. So, the negative factors of 119 are given as: Negative Factors of 119: -1, -7, -17, and -119. The factor list of 119 including positive as well as negative factors is given below. Factors of  119: 1, -1, 7, -7, 17, -17, 119, -119

### Important Properties

Following are some of the important properties of number 119 and its factors.
1. 119 is a composite number with two prime factors 7 and 17.
2. 119 is a unique number that is obtained from the sum of seven consecutive prime numbers including 7, 11, 13, 17, 19, 23, and 29.
3. The negative factors of 119 are the additive inverse of its positive factors.
4. When 119 is divided by its factor, the obtained quotient is also its factor.
5. The factors of 119 are not in the form of fractions or decimals.
6. The sum of all the factors of the number 119 is a perfect square which is 144.

## Factors of 119 by Prime Factorization

Prime Factorization is defined as the technique used to express the given number as the product of its prime factors. The technique focuses on breaking the number into its prime factors till the end product received is 1. For the prime factorization of 119, first, divide it by 7. 17 is obtained as quotient. Now, 17 cannot be divided by any other number except for 17 itself. dividing 17 by 17 will give 1 as the result which is the end of prime factorization. The prime factorization of 119 is given as:

Figure 2 – Prime factorization of 119

The prime factorization of 119 can also be expressed as:

7 x 17 = 119

7 and 17 both are prime factors of 11.

## Factor Tree of 119

A factor tree is the graphic representation of the prime factors of a number. In the case of 119, the prime numbers 7 and 17 are considered to be its prime factors. The following figure 2 shows the factor tree of the number 119:

Figure 2 – Factor tree of 119

## Factors of 119 in Pairs

Pairs of factors are the sets of numbers that consist of factors that when multiplied by one another gives the same number as their product whose factors are to be found. Similarly, the factor pairs of 119 are given as:

119 x 1 = 119

1 x 119 = 119

7 x 17 = 119

17 x 7 = 119

So, the factor pairs are (1, 119) and (7, 17). Therefore, 119 has only two positive factor pairs. The negative factor pairs can be written as (-1, -119) and (-7, -17).

## Factors of 119 Solved Examples

Let’s solve some examples to understand the methods and techniques used to find the factors of 119.

### Example 1

What are the common factors of numbers 119 and 67?

### Solution

As the number 17 is the prime number, therefore, it is clear that the number will have only two factors including 1 i.e. universal factor and the number 17 itself. Factors of 17 are given as: Factors of 17 = 1, 17 Factors of 119 are given as: Factors of 119 = 1, 7, 17, 119  So, the common factors are 1 and 17.

### Example 2

What is the sum of all the factors of number 119?

### Solution

Factors of 119 are given as: Factors of 119 = 1, 7, 17, 119 The sum of the factors is given as:

Sum = 1 + 7 + 17 + 119

Sum = 144

### Example 3

What is the highest common factor of 119 and 203?

### Solution

Factors of 119 are given as: Factors of 119 = 1, 7, 17, 119  Factors of 203 are given as: Factors of 203 = 1, 7, 29, 203  The common factors are 1 and 17. The highest common factor of 119 and 203 is 17. So, H.C.F = 17. Images/mathematical drawings are created with GeoGebra.