122 LearnersLast updated on May 26th, 2025
Factors of -14
Factors are the numbers that divide any given number evenly without a 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 -14, how they are used in real life, and tips to learn them quickly.
What are the Factors of -14?
The numbers that divide -14 evenly are known as factors of -14.
A factor of -14 is a number that divides the number without a remainder.
The positive factors of -14 are 1, 2, 7, and 14.
The negative factors of -14: -1, -2, -7, and -14.
The prime factors of 14: 2 and 7.
The prime factorization of 14 is 2 ×7.
The sum of the positive factors of 14 is 1 + 2 + 7 + 14 = 24.
How to Find Factors of -14?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify pairs of numbers that are multiplied to give 14 (since factors of -14 are the same as factors of 14 but with an opposite sign for negatives). Identifying the numbers which are multiplied to get the number 14 is the multiplication method.
Step 1: Multiply 14 by 1, 14 × 1 = 14.
Step 2: Check for other numbers that give 14 after multiplying 2 × 7 = 14
Therefore, the positive factor pairs of 14 are: (1, 14) and (2, 7). All these factor pairs result in 14.
For every positive factor, there is a negative factor.
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 14 by 1, 14 ÷ 1 = 14.
Step 2: Continue dividing 14 by the numbers until the remainder becomes 0.
14 ÷ 1 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2
14 ÷ 14 = 1
Therefore, the factors of 14 are: 1, 2, 7, 14.
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 14 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factors of 14 are 2 and 7.
The prime factorization of 14 is 2 × 7
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 14 is divided by 2 to get 7.
Step 2: Now divide 7 by 7 to get 1. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 14 is 2 × 7.
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 14: (1, 14) and (2, 7).
Negative factor pairs of -14: (-1, -14) and (-2, -7).
Common Mistakes and How to Avoid Them in Factors of -14
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
People 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 -14, 1 and 14 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -14 include -1, -2, -7, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 14/1.5 = 9.333, 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 -14 are prime numbers.
For example, 2 and 7 are the prime factors of 14, but it has other factors like 1 and 14.
Mistake 5
Mistake in Factorization
People might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 14 as 2 × 7 and missing all the key factors.
Factors of -14 Examples
Problem 1
There are 14 apples and 7 baskets. How will they divide it equally?
They will get 2 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets.
14/7 = 2
Problem 2
A rectangular garden has a total area of 14 square meters and a width of 2 meters. What is the length?
The length is 7 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
14 = length × 2
To find the value of length, we need to shift 2 to the left side.
14/2 = length
Length = 7.
Problem 3
There are 14 candies and 14 children. How many candies will each child get?
Each child will get 1 candy.
Explanation
To find the candies each child gets, divide the total candies with the children.
14/14 = 1
Problem 4
In a class, there are 2 groups and 14 students. How many students are there in each group?
There are 7 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
14/2 = 7
Problem 5
14 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each shelf has 2 books.
Explanation
Divide total books with shelves.
14/7 = 2
FAQs on Factors of -14
1.What are the factors of -14?
2.Mention the prime factors of 14.
3.Is 14 a multiple of 2?
4.Mention the factor pairs of -14?
5.What is the square of 14?
Important Glossaries for Factor of -14
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -14 are 1, 2, 7, 14, -1, -2, -7, and -14.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 14.
- 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 -14 are (1, 14), (2, 7), etc.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -7, and -14 are negative factors of -14.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 14 is 2 × 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.
