117 LearnersLast updated on May 26th, 2025
Factors of -34
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 -34, how they are used in real life, and tips to learn them quickly.
What are the Factors of -34?
The numbers that divide -34 evenly are known as factors of -34.
A factor of -34 is a number that divides the number without remainder.
The factors of -34 are 1, 2, 17, and 34.
Negative factors of -34: -1, -2, -17, and -34.
Prime factors of -34: 2 and 17.
Prime factorization of -34: -1 × 2 × 17.
The sum of positive factors of -34: 1 + 2 + 17 + 34 = 54
How to Find Factors of -34?
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 -34. Identifying the numbers which are multiplied to get the number -34 is the multiplication method.
Step 1: Multiply -34 by 1, -34 × 1 = -34.
Step 2: Check for other numbers that give -34 after multiplying 2 × -17 = -34
-2 × 17 = -34
Therefore, the positive factor pairs of -34 are: (1, -34), (2, -17).
All these factor pairs result in -34.
For every positive factor, there is a corresponding 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 -34 by 1, -34 ÷ 1 = -34.
Step 2: Continue dividing -34 by the numbers until the remainder becomes 0.
-34 ÷ 1 = -34
-34 ÷ 2 = -17
-34 ÷ 17 = -2
-34 ÷ 34 = -1
Therefore, the factors of -34 are: 1, 2, 17, 34.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 -34 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-34 ÷ -1 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1
The prime factors of -34 are 2 and 17.
The prime factorization of -34 is: -1 × 2 × 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, -34 is divided by -1 to get 34.
Step 2: Now divide 34 by 2 to get 17.
Step 3: Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of -34 is: -1 × 2 × 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 -34: (1, -34), (2, -17).
Negative factor pairs of -34: (-1, 34), (-2, 17).
Common Mistakes and How to Avoid Them in Factors of -34
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 -34, 1 and -34 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 -34 consist of -1, -2, -17, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because -34/1.5 = -22.666, 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 -34 are prime numbers. For example, 2 and 17 are the prime factors of -34, but it has other factors like 1, 34.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -34 as -1 × 2 × 17 and missing all the key factors.
Factors of -34 Examples
Problem 1
There are 34 apples and 2 baskets. How will they divide it equally?
They will get 17 apples in each basket.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
34/2 = 17
Problem 2
A rectangular garden has a width of 2 meters and a total area of 34 square meters. Find the length.
17 meters.
Explanation
To find the length of the garden, we use the formula, Area = length × width
34 = length × 2
To find the value of length, we need to shift 2 to the left side.
34/2 = length
Length = 17.
Problem 3
There are 17 people and 34 candies. How many candies will each person get if divided equally?
Each person will get 2 candies.
Explanation
To find the candies each person will get, divide the total candies by the people.
34/17 = 2
Problem 4
In a class, there are 34 chairs, and 2 rows. How many chairs are there in each row?
There are 17 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
34/2 = 17
Problem 5
34 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 17 books.
Explanation
Divide total books by shelves.
34/2 = 17
FAQs on Factors of -34
1.What are the factors of -34?
2.Mention the prime factors of -34.
3.Is -34 a multiple of 2?
4.Mention the factor pairs of -34.
5.What is the square of 34?
Important Glossaries for Factors of -34
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -34 are 1, 2, 17, and 34.
- Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of -34.
- 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 -34 are (1, -34), (2, -17), etc.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -17, and -34 are negative factors of -34.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of -34 is -1 × 2 × 17.
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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.
