115 LearnersLast updated on May 26th, 2025
Factors of 1014
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 1014, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1014?
The numbers that divide 1014 evenly are known as factors of 1014.
A factor of 1014 is a number that divides the number without remainder.
The factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, and 1014.
Negative factors of 1014: -1, -2, -3, -6, -13, -26, -39, -78, -169, -338, -507, and -1014.
Prime factors of 1014: 2, 3, and 13.
Prime factorization of 1014: 2 × 3 × 13 × 13.
The sum of factors of 1014: 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 + 169 + 338 + 507 + 1014 = 2196
How to Find Factors of 1014?
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 1014. Identifying the numbers which are multiplied to get the number 1014 is the multiplication method.
Step 1: Multiply 1014 by 1, 1014 × 1 = 1014.
Step 2: Check for other numbers that give 1014 after multiplying
2 × 507 = 1014
3 × 338 = 1014
6 × 169 = 1014
13 × 78 = 1014
26 × 39 = 1014
Therefore, the positive factor pairs of 1014 are: (1, 1014), (2, 507), (3, 338), (6, 169), (13, 78), (26, 39).
All these factor pairs result in 1014.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1014 by 1, 1014 ÷ 1 = 1014.
Step 2: Continue dividing 1014 by the numbers until the remainder becomes 0.
1014 ÷ 1 = 1014
1014 ÷ 2 = 507
1014 ÷ 3 = 338
1014 ÷ 6 = 169
1014 ÷ 13 = 78
1014 ÷ 26 = 39
Therefore, the factors of 1014 are: 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014.
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 1014 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1014 ÷ 2 = 507
507 ÷ 3 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
The prime factors of 1014 are 2, 3, and 13.
The prime factorization of 1014 is: 2 × 3 × 13 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1014 is divided by 2 to get 507.
Step 2: Now divide 507 by 3 to get 169.
Step 3: Then divide 169 by 13 to get 13. Here, 13 is the smallest prime number and cannot be divided anymore. So, the prime factorization of 1014 is: 2 × 3 × 13 × 13.
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 1014: (1, 1014), (2, 507), (3, 338), (6, 169), (13, 78), (26, 39).
Negative factor pairs of 1014: (-1, -1014), (-2, -507), (-3, -338), (-6, -169), (-13, -78), (-26, -39).
Common Mistakes and How to Avoid Them in Factors of 1014
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 1014, 1 and 1014 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1014 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1014/1.5 = 676, 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 1014 are prime numbers.
For example, 2, 3, and 13 are the prime factors of 1014, but it has other factors like 6, 39.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1014 as 2 × 3 × 13 × 13 and missing all the key factors.
Factors of 1014 Examples
Problem 1
A book club has 6 members and 1014 books. How many books will each member receive if they are divided equally?
Each member will receive 169 books.
Explanation
To divide the books equally, we need to divide the total books by the number of members.
1014/6 = 169
Problem 2
A rectangle has a length of 13 meters and an area of 1014 square meters. How wide is the rectangle?
78 meters.
Explanation
To find the width of the rectangle, we use the formula,
Area = length × width
1014 = 13 × width
To find the value of width, we need to shift 13 to the left side.
1014/13 = width
Width = 78.
Problem 3
There are 39 boxes and 1014 marbles. How many marbles will be in each box?
Each box will have 26 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1014/39 = 26
Problem 4
A classroom has 1014 chairs arranged in 3 rows. How many chairs are in each row?
There are 338 chairs in each row.
Explanation
Dividing the chairs by the number of rows, we will get the number of chairs in each row.
1014/3 = 338
Problem 5
1014 pages need to be printed in 2 printers. How many pages will each printer handle?
Each printer will handle 507 pages.
Explanation
Divide the total pages by the number of printers.
1014/2 = 507
FAQs on Factors of 1014
1.What are the factors of 1014?
2.Mention the prime factors of 1014.
3.Is 1014 a multiple of 13?
4.Mention the factor pairs of 1014?
5.What is the square of 1014?
Important Glossaries for Factor of 1014
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, and 1014.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 1014.
- 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 1014 are (1, 1014), (2, 507), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1014 is 2 × 3 × 13 × 13.
- Multiples: Numbers that are the product of a given number and an integer. For example, 1014 is a multiple of 13.
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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.
