100 LearnersLast updated on May 26th, 2025
Factors of 1278
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 1278, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1278?
The numbers that divide 1278 evenly are known as factors of 1278.
A factor of 1278 is a number that divides the number without remainder.
The factors of 1278 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 639, and 1278.
Negative factors of 1278: -1, -2, -3, -6, -11, -17, -22, -33, -34, -51, -66, -102, -187, -374, -639, and -1278.
Prime factors of 1278: 2, 3, 11, 17.
Prime factorization of 1278: 2 × 3 × 11 × 17.
The sum of factors of 1278: 1 + 2 + 3 + 6 + 11 + 17 + 22 + 33 + 34 + 51 + 66 + 102 + 187 + 374 + 639 + 1278 = 2826
How to Find Factors of 1278?
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 1278. Identifying the numbers which are multiplied to get the number 1278 is the multiplication method.
Step 1: Multiply 1278 by 1, 1278 × 1 = 1278.
Step 2: Check for other numbers that give 1278 after multiplying
2 × 639 = 1278
3 × 426 = 1278
6 × 213 = 1278
11 × 116 = 1278
17 × 75 = 1278
22 × 58 = 1278
33 × 38 = 1278
Therefore, the positive factor pairs of 1278 are: (1, 1278), (2, 639), (3, 426), (6, 213), (11, 116), (17, 75), (22, 58), (33, 38).
All these factor pairs result in 1278.
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 1278 by 1, 1278 ÷ 1 = 1278.
Step 2: Continue dividing 1278 by the numbers until the remainder becomes 0.
1278 ÷ 1 = 1278
1278 ÷ 2 = 639
1278 ÷ 3 = 426
1278 ÷ 6 = 213
1278 ÷ 11 = 116
1278 ÷ 17 = 75
1278 ÷ 22 = 58
1278 ÷ 33 = 38
Therefore, the factors of 1278 are: 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 639, and 1278.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1278 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1278 ÷ 2 = 639
639 ÷ 3 = 213
213 ÷ 3 = 71
71 ÷ 71 = 1
The prime factors of 1278 are 2, 3, 11, and 17.
The prime factorization of 1278 is: 2 × 3 × 11 × 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, 1278 is divided by 2 to get 639.
Step 2: Now divide 639 by 3 to get 213.
Step 3: Then divide 213 by 3 to get 71.
Step 4: Divide 71 by 71 to get 1.
Here, 71 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1278 is: 2 × 3 × 11 × 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 1278: (1, 1278), (2, 639), (3, 426), (6, 213), (11, 116), (17, 75), (22, 58), (33, 38).
Negative factor pairs of 1278: (-1, -1278), (-2, -639), (-3, -426), (-6, -213), (-11, -116), (-17, -75), (-22, -58), (-33, -38).
Common Mistakes and How to Avoid Them in Factors of 1278
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 1278, 1 and 1278 are also factors.
Factors of 1278 Examples
Problem 1
There are 3 siblings and 1278 candies. How will they divide it equally?
They will get 426 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of siblings.
1278/3 = 426
Problem 2
A rectangular garden has a length of 22 meters and a total area of 1278 square meters. Find the width?
58 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1278 = 22 × width
To find the value of width, we need to shift 22 to the left side.
1278/22 = width
Width = 58.
Problem 3
There are 6 boxes and 1278 marbles. How many marbles will be in each box?
Each box will have 213 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1278/6 = 213
Problem 4
In a class, there are 11 groups and 1278 students. How many students are there in each group?
There are 116 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1278/11 = 116
Problem 5
1278 books need to be arranged in 17 shelves. How many books will go on each shelf?
Each of the shelves has 75 books.
Explanation
Divide total books by shelves.
1278/17 = 75
FAQs on Factors of 1278
1.What are the factors of 1278?
2.Mention the prime factors of 1278.
3.Is 1278 a multiple of 6?
4.Mention the factor pairs of 1278?
5.What is the square of 1278?
Important Glossaries for Factors of 1278
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1278 are 1, 2, 3, 6, etc.
Prime Factors: The factors which are prime numbers. For example, 2, 3, 11, and 17 are prime factors of 1278.
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 1278 are (1, 1278), (2, 639), etc.
Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1278 is 2 × 3 × 11 × 17.
Divisibility: A number is divisible by another if the division results in a whole number without a remainder. For example, 1278 is divisible by 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.
