100 LearnersLast updated on May 26th, 2025
Factors of 1078
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 1078, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1078?
The numbers that divide 1078 evenly are known as factors of 1078.
A factor of 1078 is a number that divides the number without a remainder.
The factors of 1078 are 1, 2, 7, 14, 77, 154, 539, and 1078.
Negative factors of 1078: -1, -2, -7, -14, -77, -154, -539, and -1078.
Prime factors of 1078: 2 and 7.
Prime factorization of 1078: 2 × 7 × 77.
The sum of factors of 1078: 1 + 2 + 7 + 14 + 77 + 154 + 539 + 1078 = 1872
How to Find Factors of 1078?
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 1078. Identifying the numbers which are multiplied to get the number 1078 is the multiplication method.
Step 1: Multiply 1078 by 1, 1078 × 1 = 1078
Step 2: Check for other numbers that give 1078 after multiplying
2 × 539 = 1078
7 × 154 = 1078
14 × 77 = 1078
Therefore, the positive factor pairs of 1078 are: (1, 1078), (2, 539), (7, 154), (14, 77).
All these factor pairs result in 1078.
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 1078 by 1, 1078 ÷ 1 = 1078.
Step 2: Continue dividing 1078 by the numbers until the remainder becomes 0.
1078 ÷ 1 = 1078
1078 ÷ 2 = 539
1078 ÷ 7 = 154
1078 ÷ 14 = 77
Therefore, the factors of 1078 are: 1, 2, 7, 14, 77, 154, 539, 1078.
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 1078 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1078 ÷ 2 = 539
539 ÷ 7 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 1078 are 2, 7, and 11.
The prime factorization of 1078 is: 2 × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1078 is divided by 2 to get 539.
Step 2: Now divide 539 by 7 to get 77.
Step 3: Then divide 77 by 7 to get 11.
Here, 11 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1078 is: 2 × 7 × 11.
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 1078: (1, 1078), (2, 539), (7, 154), and (14, 77).
Negative factor pairs of 1078: (-1, -1078), (-2, -539), (-7, -154), and (-14, -77).
Common Mistakes and How to Avoid Them in Factors of 1078
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1078, 1 and 1078 are also factors.
Factors of 1078 Examples
Problem 1
There are 7 teams and 1078 points to be distributed equally. How many points will each team get?
They will get 154 points each.
Explanation
To distribute the points equally, we need to divide the total points with the number of teams.
1078/7 = 154
Problem 2
A rectangular garden has a length of 77 meters and a total area of 1078 square meters. Find the width.
14 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1078 = 77 × width
To find the value of width, we need to shift 77 to the left side.
1078/77 = width
Width = 14.
Problem 3
There are 154 chairs and 1078 guests. How many guests will be seated on each chair?
Each chair will have 7 guests.
Explanation
To find the guests on each chair, divide the total guests with the chairs.
1078/154 = 7
Problem 4
In a conference, there are 1078 participants, and 14 workshops. How many participants are there in each workshop?
There are 77 participants in each workshop.
Explanation
Dividing the participants with the total workshops, we will get the number of participants in each workshop.
1078/14 = 77
Problem 5
1078 boxes need to be arranged in 2 warehouses. How many boxes will go in each warehouse?
Each of the warehouses will have 539 boxes.
Explanation
Divide total boxes with the warehouses.
1078/2 = 539
FAQs on Factors of 1078
1.What are the factors of 1078?
2.Mention the prime factors of 1078.
3.Is 1078 a multiple of 7?
4.Mention the factor pairs of 1078?
5.What is the square of 1078?
6.How can children in Canada use numbers in everyday life to understand Factors of 1078?
7.What are some fun ways kids in Canada can practice Factors of 1078 with numbers?
8.What role do numbers and Factors of 1078 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1078 skills?
Important Glossaries for Factor of 1078
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1078 are 1, 2, 7, 14, 77, 154, 539, and 1078.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 11 are prime factors of 1078.
- 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 1078 are (1, 1078), (2, 539), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1078 is 2 × 7 × 11.
- Division method: A method of finding factors by dividing the number by integers until the remainder is zero. For example, dividing 1078 by 2 gives a factor of 539.
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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
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