114 LearnersLast updated on May 26th, 2025
Factors of -119
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -119, how they are used in real life, and tips to learn them quickly.
What are the Factors of -119?
The numbers that divide -119 evenly are known as factors of -119.
A factor of -119 is a number that divides the number without remainder.
The factors of -119: 1, -1, 7, -7, 17, -17, 119, and -119.
Prime factors of 119: 7 and 17.
Prime factorization of 119: 7 × 17.
How to Find Factors of -119?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -119. Identifying the numbers which are multiplied to get the number -119 is the multiplication method.
Step 1: Multiply -119 by 1, -119 × 1 = -119.
Step 2: Check for other numbers that give -119 after multiplying
-1 × 119 = -119
7 × -17 = -119
-7 × 17 = -119
Therefore, the positive factor pairs of -119 are: (1, -119), (-1, 119), (7, -17), (-7, 17).
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide -119 by 1, -119 ÷ 1 = -119.
Step 2: Continue dividing -119 by the numbers until the remainder becomes 0.
-119 ÷ 1 = -119
-119 ÷ -1 = 119
-119 ÷ 7 = -17
-119 ÷ -7 = 17
Therefore, the factors of -119 are: 1, -1, 7, -7, 17, -17, 119, -119.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 119 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
119 ÷ 7 = 17
17 ÷ 17 = 1
The prime factors of 119 are 7 and 17.
The prime factorization of 119 is: 7 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 119 is divided by 7 to get 17.
Step 2: Now divide 17 by 17 to get 1. Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 119 is: 7 × 17.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of -119: (1, -119), (7, -17).
Negative factor pairs of -119: (-1, 119), (-7, 17).
Common Mistakes and How to Avoid Them in Factors of -119
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -119, 1 and -119 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -119 consist of -1, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -119/1.5 = -79.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of -119 are prime numbers.
For example, 7 and 17 are the prime factors of -119, but it has other factors like 1, 119.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 119 as 7 × 17 and missing all the key factors.
Factors of -119 Examples
Problem 1
A team lost 119 points due to penalties. If each penalty cost them 17 points, how many penalties did they incur?
They incurred 7 penalties.
Explanation
To find the number of penalties, divide the total points lost by the points per penalty.
119/17 = 7
Problem 2
A construction company has 119 bricks. They need to place them in stacks of 7 bricks each. How many stacks will they have?
They will have 17 stacks.
Explanation
To find the number of stacks, divide the total bricks by the number of bricks per stack.
119/7 = 17
Problem 3
There are 119 students in a school, and they need to form groups with 1 teacher per group, with each group having 17 students. How many groups are there?
There are 7 groups.
Explanation
To find the number of groups, divide the total students by the number of students per group.
119/17 = 7
Problem 4
A gardener has 119 plants and wants to plant them in rows of 7. How many rows will there be?
There will be 17 rows.
Explanation
Dividing the total number of plants by the number of plants per row, we get the number of rows.
119/7 = 17
Problem 5
A baker made 119 cookies and plans to package them in boxes of 17 cookies each. How many boxes will she need?
She will need 7 boxes.
Explanation
Divide the total cookies by the number of cookies per box.
119/17 = 7
FAQs on Factors of -119
1.What are the factors of -119?
2.Mention the prime factors of -119.
3.Is 119 a multiple of 7?
4.Mention the factor pairs of -119?
5.What is the absolute value of -119?
Important Glossaries for Factors of -119
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -119 are 1, -1, 7, -7, 17, -17, 119, and -119.
- Prime factors: The factors which are prime numbers. For example, 7 and 17 are prime factors of 119.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of -119 are (1, -119), (-1, 119), etc.
- Prime factorization: Breaking down a number into its basic prime number components. For example, the prime factorization of 119 is 7 × 17.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 119 is a multiple of 7.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
