102 LearnersLast updated on May 26th, 2025
Factors of 2014
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 2014, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2014?
The numbers that divide 2014 evenly are known as factors of 2014.
A factor of 2014 is a number that divides the number without remainder.
The factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, and 2014.
Negative factors of 2014: -1, -2, -19, -38, -53, -106, -1007, and -2014.
Prime factors of 2014: 2, 19, and 53.
Prime factorization of 2014: 2 × 19 × 53.
The sum of factors of 2014: 1 + 2 + 19 + 38 + 53 + 106 + 1007 + 2014 = 3240
How to Find Factors of 2014?
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 2014. Identifying the numbers which are multiplied to get the number 2014 is the multiplication method.
Step 1: Multiply 2014 by 1, 2014 × 1 = 2014.
Step 2: Check for other numbers that give 2014 after multiplying
2 × 1007 = 2014
19 × 106 = 2014
38 × 53 = 2014
Therefore, the positive factor pairs of 2014 are: (1, 2014), (2, 1007), (19, 106), (38, 53).
All these factor pairs result in 2014.
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 2014 by 1, 2014 ÷ 1 = 2014.
Step 2: Continue dividing 2014 by the numbers until the remainder becomes 0.
2014 ÷ 1 = 2014
2014 ÷ 2 = 1007
2014 ÷ 19 = 106
2014 ÷ 38 = 53
Therefore, the factors of 2014 are: 1, 2, 19, 38, 53, 106, 1007, 2014.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 2014 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2014 ÷ 2 = 1007
1007 ÷ 19 = 53
53 ÷ 53 = 1
The prime factors of 2014 are 2, 19, and 53.
The prime factorization of 2014 is: 2 × 19 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 2014 is divided by 2 to get 1007.
Step 2: Now divide 1007 by 19 to get 53.
Step 3: Divide 53 by 53 to get 1. Here, 53 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2014 is: 2 × 19 × 53.
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 2014: (1, 2014), (2, 1007), (19, 106), and (38, 53).
Negative factor pairs of 2014: (-1, -2014), (-2, -1007), (-19, -106), and (-38, -53).
Common Mistakes and How to Avoid Them in Factors of 2014
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 number. Always remember to include 1 and the number itself.
For example, in factors of 2014, 1 and 2014 are also factors.
Factors of 2014 Examples
Problem 1
There are 19 people and 2014 apples. How will they divide them equally?
They will get 106 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
2014/19 = 106
Problem 2
A field is rectangular, the length of the field is 53 meters and the total area is 2014 square meters. Find the width?
38 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
2014 = 53 × width
To find the value of width, we need to shift 53 to the left side.
2014/53 = width
Width = 38.
Problem 3
There are 2 buses and 2014 passengers. How many passengers will be in each bus?
Each bus will have 1007 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the number of buses.
2014/2 = 1007
Problem 4
In a class, there are 2014 students, and 53 groups. How many students are there in each group?
There are 38 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
2014/53 = 38
Problem 5
2014 books need to be arranged in 19 shelves. How many books will go on each shelf?
Each of the shelves has 106 books.
Explanation
Divide total books by shelves.
2014/19 = 106
FAQs on Factors of 2014
1.What are the factors of 2014?
2.Mention the prime factors of 2014.
3.Is 2014 a multiple of 19?
4.Mention the factor pairs of 2014?
5.What is the square of 2014?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 2014?
7.What are some fun ways kids in Indonesia can practice Factors of 2014 with numbers?
8.What role do numbers and Factors of 2014 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 2014 skills?
Important Glossaries for Factors of 2014
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, and 2014.
- Prime factors: The factors which are prime numbers. For example, 2, 19, and 53 are prime factors of 2014.
- 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 2014 are (1, 2014), (2, 1007), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 2014 is 2 × 19 × 53.
- Multiples: A multiple of a number is the product of that number and an integer. For example, 2014 is a multiple of 19.
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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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