100 LearnersLast updated on May 27th, 2025
Factors of 678
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 678, how they are used in real life, and tips to learn them quickly.
What are the Factors of 678?
The numbers that divide 678 evenly are known as factors of 678.
A factor of 678 is a number that divides the number without remainder.
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, and 678.
Negative factors of 678: -1, -2, -3, -6, -113, -226, -339, and -678.
Prime factors of 678: 2, 3, and 113.
Prime factorization of 678: 2 × 3 × 113.
The sum of factors of 678: 1 + 2 + 3 + 6 + 113 + 226 + 339 + 678 = 1368
How to Find Factors of 678?
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 678. Identifying the numbers which are multiplied to get the number 678 is the multiplication method.
Step 1: Multiply 678 by 1, 678 × 1 = 678.
Step 2: Check for other numbers that give 678 after multiplying
2 × 339 = 678
3 × 226 = 678
6 × 113 = 678
Therefore, the positive factor pairs of 678 are: (1, 678), (2, 339), (3, 226), (6, 113). 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 678 by 1, 678 ÷ 1 = 678.
Step 2: Continue dividing 678 by the numbers until the remainder becomes 0.
678 ÷ 1 = 678
678 ÷ 2 = 339
678 ÷ 3 = 226
678 ÷ 6 = 113
Therefore, the factors of 678 are: 1, 2, 3, 6, 113, 226, 339, 678.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 678 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
678 ÷ 2 = 339
339 ÷ 3 = 113
113 ÷ 113 = 1
The prime factors of 678 are 2, 3, and 113.
The prime factorization of 678 is: 2 × 3 × 113.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 678 is divided by 2 to get 339.
Step 2: Now divide 339 by 3 to get 113. Here, 113 is a prime number, which cannot be divided further. So, the prime factorization of 678 is: 2 × 3 × 113.
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 678: (1, 678), (2, 339), (3, 226), (6, 113).
Negative factor pairs of 678: (-1, -678), (-2, -339), (-3, -226), (-6, -113).
Common Mistakes and How to Avoid Them in Factors of 678
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 678, 1 and 678 are also factors.
Factors of 678 Examples
Problem 1
There are 6 teams and 678 points. How will they divide them equally?
They will get 113 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
678/6 = 113
Problem 2
A garden is rectangular, the length of the garden is 3 meters and the total area is 678 square meters. Find the width?
226 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
678 = 3 × width
To find the value of width, we need to shift 3 to the left side.
678/3 = width
Width = 226.
Problem 3
There are 113 baskets and 678 apples. How many apples will be in each basket?
Each basket will have 6 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
678/113 = 6
Problem 4
In a class, there are 678 students, and 2 groups. How many students are there in each group?
There are 339 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
678/2 = 339
Problem 5
678 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 226 books.
Explanation
Divide total books by shelves.
678/3 = 226
FAQs on Factors of 678
1.What are the factors of 678?
2.Mention the prime factors of 678.
3.Is 678 a multiple of 3?
4.Mention the factor pairs of 678?
5.What is the square of 678?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 678?
7.What are some fun ways kids in United Kingdom can practice Factors of 678 with numbers?
8.What role do numbers and Factors of 678 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 678 skills?
Important Glossaries for Factor of 678
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 678 are 1, 2, 3, 6, 113, 226, 339, and 678.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 113 are prime factors of 678.
- 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 678 are (1, 678), (2, 339), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 678 is 2 × 3 × 113.
- Multiple: A number that can be divided by another number without a remainder. For example, 678 is a multiple of 3.
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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.
