118 LearnersLast updated on May 26th, 2025
Factors of -68
Factors are 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 -68, how they are used in real life, and tips to learn them quickly.
What are the Factors of -68?
The numbers that divide -68 evenly are known as factors of -68.
A factor of -68 is a number that divides the number without a remainder.
The positive factors of 68 are 1, 2, 4, 17, 34, and 68.
The negative factors of -68: -1, -2, -4, -17, -34, and -68.
Prime factors of 68: 2 and 17.
Prime factorization of 68: 2² × 17.
The sum of positive factors of 68: 1 + 2 + 4 + 17 + 34 + 68 = 126
How to Find Factors of -68?
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 identify the pairs of numbers that multiply to give 68. Identifying the numbers that are multiplied to get the number 68 is the multiplication method.
Step 1: Multiply 68 by 1, 68 × 1 = 68.
Step 2: Check for other numbers that give 68 after multiplying 2 × 34 = 68 4 × 17 = 68
Therefore, the positive factor pairs of 68 are: (1, 68), (2, 34), and (4, 17).
All these factor pairs result in 68.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 68 by 1, 68 ÷ 1 = 68.
Step 2: Continue dividing 68 by the numbers until the remainder becomes 0.
68 ÷ 1 = 68
68 ÷ 2 = 34
68 ÷ 4 = 17
Therefore, the factors of 68 are: 1, 2, 4, 17, 34, 68.
Prime Factors and Prime Factorization
The factors can be found by dividing it by prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 68 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.
68 ÷ 2 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1
The prime factors of 68 are 2 and 17.
The prime factorization of 68 is: 2² × 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, 68 is divided by 2 to get 34.
Step 2: Now divide 34 by 2 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 68 is: 2² × 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 68: (1, 68), (2, 34), and (4, 17).
Negative factor pairs of -68: (-1, -68), (-2, -34), and (-4, -17).
Common Mistakes and How to Avoid Them in Factors of -68
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 68, 1 and 68 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 -68 consist of -1, -2, -4, 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 68/1.5 = 45.333, 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 68 are prime numbers.
For example, 2 and 17 are the prime factors of 68, but it has other factors like 4, 34.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 68 as 2² × 17 and missing all the key factors.
Factors of -68 Examples
Problem 1
There are 4 friends and 68 marbles. How will they divide them equally?
They will get 17 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
68/4 = 17
Problem 2
A garden is rectangular, the length of the garden is 17 meters, and the total area is 68 square meters. Find the width.
4 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 68 = 17 × width
To find the value of width, we need to shift 17 to the left side.
68/17 = width
Width = 4.
Problem 3
There are 2 baskets and 68 apples. How many apples will be in each basket?
Each basket will have 34 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
68/2 = 34
Problem 4
In a class, there are 68 pencils, and 4 boxes. How many pencils are there in each box?
There are 17 pencils in each box.
Explanation
Dividing the pencils by the total boxes, we will get the number of pencils in each box.
68/4 = 17
Problem 5
68 chairs need to be arranged in 2 rows. How many chairs will go in each row?
Each row has 34 chairs.
Explanation
Divide total chairs by rows.
68/2 = 34
FAQs on Factors of -68
1.What are the factors of -68?
2.Mention the prime factors of 68.
3.Is 68 a multiple of 4?
4.Mention the factor pairs of -68?
5.What is the square of 68?
Important Glossaries for Factors of -68
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 68 are 1, 2, 4, 17, 34, and 68.
- Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of 68.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 68 is 2² × 17.
- 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 68 are (1, 68), (2, 34), etc.
- Negative factors: Factors that are negative counterparts of the positive factors. For example, -1, -2, -4, -17, -34, and -68 are the negative factors of -68.
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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.
