100 LearnersLast updated on May 26th, 2025
Factors of -294
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 -294, how they are used in real life, and tips to learn them quickly.
What are the Factors of -294?
The numbers that divide -294 evenly are known as factors of -294.
A factor of -294 is a number that divides the number without remainder.
The positive factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294.
Therefore, the factors of -294 include all these numbers and their negatives: -1, -2, -3, -6, -7, -14, -21, -42, -49, -98, -147, and -294.
Prime factors of 294: 2, 3, and 7.
Prime factorization of 294: 2 × 3 × 7².
The sum of the positive factors of 294: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 + 49 + 98 + 147 + 294 = 684
How to Find Factors of -294?
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 the pairs of numbers that are multiplied to give 294 (ignoring the negative sign initially). Identifying the numbers which are multiplied to get the number 294 is the multiplication method.
Step 1: Multiply 294 by 1, 294 × 1 = 294.
Step 2: Check for other numbers that give 294 after multiplying:
2 × 147 = 294
3 × 98 = 294
6 × 49 = 294
7 × 42 = 294
14 × 21 = 294
Therefore, the positive factor pairs of 294 are: (1, 294), (2, 147), (3, 98), (6, 49), (7, 42), and (14, 21).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 294 by 1, 294 ÷ 1 = 294.
Step 2: Continue dividing 294 by the numbers until the remainder becomes 0.
294 ÷ 1 = 294
294 ÷ 2 = 147
294 ÷ 3 = 98
294 ÷ 6 = 49
294 ÷ 7 = 42
Therefore, the factors of 294 are: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294.
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 294 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
294 ÷ 2 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 294 are 2, 3, and 7.
The prime factorization of 294 is: 2 × 3 × 7².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 294 is divided by 2 to get 147.
Step 2: Now divide 147 by 3 to get 49.
Step 3: Then divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 294 is: 2 × 3 × 7².
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 294: (1, 294), (2, 147), (3, 98), (6, 49), (7, 42), and (14, 21).
Negative factor pairs of -294: (-1, -294), (-2, -147), (-3, -98), (-6, -49), (-7, -42), and (-14, -21).
Common Mistakes and How to Avoid Them in Factors of -294
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -294, 1 and 294 are also factors.
Factors of -294 Examples
Problem 1
There are 14 people and -294 apples. How will they divide it equally?
They will get -21 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
-294/14 = -21
Problem 2
A rectangular field has a width of 7 meters and a total area of 294 square meters. Find the length.
42 meters.
Explanation
To find the length of the field, we use the formula,
Area = length × width
294 = length × 7
To find the value of length, we need to shift 7 to the left side.
294/7 = length
Length = 42.
Problem 3
There are 42 baskets and -294 oranges. How many oranges will be in each basket?
Each basket will have -7 oranges.
Explanation
To find the oranges in each basket, divide the total oranges by the baskets.
-294/42 = -7
Problem 4
In a class, there are 294 students, and 49 groups. How many students are there in each group?
There are 6 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
294/49 = 6
Problem 5
294 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each shelf will have 49 books.
Explanation
Divide total books by shelves.
294/6 = 49
FAQs on Factors of -294
1.What are the factors of -294?
2.Mention the prime factors of -294.
3.Is 294 a multiple of 7?
4.Mention the factor pairs of -294.
5.What is the square of 294?
6.How can children in India use numbers in everyday life to understand Factors of -294?
7.What are some fun ways kids in India can practice Factors of -294 with numbers?
8.What role do numbers and Factors of -294 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -294 skills?
Important Glossaries for Factor of -294
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -294 include 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294, along with their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of -294.
- 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 294 include (1, 294), (2, 147), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 294 is 2 × 3 × 7².
- Multiple: A number that can be divided by another number without a remainder. For example, 294 is a multiple of 7.
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About BrightChamps in India
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.
