119 LearnersLast updated on May 26th, 2025
Factors of 1678
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 1678, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1678?
The numbers that divide 1678 evenly are known as factors of 1678.
A factor of 1678 is a number that divides the number without remainder.
The factors of 1678 are 1, 2, 839, and 1678.
Negative factors of 1678: -1, -2, -839, and -1678.
Prime factors of 1678: 2 and 839.
Prime factorization of 1678: 2 × 839.
The sum of factors of 1678: 1 + 2 + 839 + 1678 = 2520
How to Find Factors of 1678?
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 1678. Identifying the numbers which are multiplied to get the number 1678 is the multiplication method.
Step 1: Multiply 1678 by 1, 1678 × 1 = 1678.
Step 2: Check for other numbers that give 1678 after multiplying 2 × 839 = 1678
Therefore, the positive factor pairs of 1678 are: (1, 1678), (2, 839). All these factor pairs result in 1678.
For every positive factor, there is a 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 1678 by 1, 1678 ÷ 1 = 1678.
Step 2: Continue dividing 1678 by the numbers until the remainder becomes 0.
1678 ÷ 1 = 1678
1678 ÷ 2 = 839
Therefore, the factors of 1678 are: 1, 2, 839, 1678.
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 1678 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1678 ÷ 2 = 839
839 is a prime number, so we stop here.
The prime factors of 1678 are 2 and 839.
The prime factorization of 1678 is: 2 × 839.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1678 is divided by 2 to get 839. 839 is a prime number and cannot be divided anymore. So, the prime factorization of 1678 is: 2 × 839.
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 1678: (1, 1678), (2, 839).
Negative factor pairs of 1678: (-1, -1678), (-2, -839).
Common Mistakes and How to Avoid Them in Factors of 1678
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 1678, 1 and 1678 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1678 consist of -1, -2, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1678/1.5 = 1118.67, 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 1678 are prime numbers. For example, 2 and 839 are the prime factors of 1678, but it has other factors like 1 and 1678.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1678 as 2 × 839 and missing all the key factors.
Factors of 1678 Examples
Problem 1
There are 2 teams and 1678 points. How will they divide the points equally?
They will get 839 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
1678/2 = 839
Problem 2
A fence is 1678 meters long and needs to be divided into segments of 839 meters each. How many segments will there be?
There will be 2 segments.
Explanation
To find the number of segments, we divide the total length of the fence by the length of each segment.
1678/839 = 2
Problem 3
There are 1678 apples to be packed into 839 boxes. How many apples will be in each box?
Each box will have 2 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1678/839 = 2
Problem 4
A classroom has 1678 chairs and 2 rows. How many chairs are there in each row?
There are 839 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
1678/2 = 839
Problem 5
1678 plants need to be arranged in 839 pots. How many plants will go in each pot?
Each pot will have 2 plants.
Explanation
Divide total plants by pots.
1678/839 = 2
FAQs on Factors of 1678
1.What are the factors of 1678?
2.Mention the prime factors of 1678.
3.Is 1678 a multiple of 2?
4.Mention the factor pairs of 1678?
5.What is the square of 1678?
6.How can children in United States use numbers in everyday life to understand Factors of 1678?
7.What are some fun ways kids in United States can practice Factors of 1678 with numbers?
8.What role do numbers and Factors of 1678 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1678 skills?
Important Glossaries for Factor of 1678
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1678 are 1, 2, 839, and 1678.
- Prime factors: The factors which are prime numbers. For example, 2 and 839 are prime factors of 1678.
- 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 1678 are (1, 1678) and (2, 839).
- Prime factorization: The expression of a number as a product of its prime factors. The prime factorization of 1678 is 2 × 839.
- Multiples: Numbers that can be divided by the original number without leaving a remainder. For example, 3356 and 5034 are multiples of 1678.
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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.
