141 LearnersLast updated on May 28th, 2025
Factors of 1314
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 1314, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1314?
The numbers that divide 1314 evenly are known as factors of 1314.
A factor of 1314 is a number that divides the number without remainder.
The factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, and 1314.
Negative factors of 1314: -1, -2, -3, -6, -9, -18, -73, -146, -219, -438, -657, and -1314.
Prime factors of 1314: 2, 3, and 73.
Prime factorization of 1314: 2 × 3 × 3 × 73.
The sum of factors of 1314: 1 + 2 + 3 + 6 + 9 + 18 + 73 + 146 + 219 + 438 + 657 + 1314 = 2886
How to Find Factors of 1314?
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 1314. Identifying the numbers which are multiplied to get the number 1314 is the multiplication method.
Step 1: Multiply 1314 by 1, 1314 × 1 = 1314.
Step 2: Check for other numbers that give 1314 after multiplying
2 × 657 = 1314
3 × 438 = 1314
6 × 219 = 1314
9 × 146 = 1314
18 × 73 = 1314
Therefore, the positive factor pairs of 1314 are: (1, 1314), (2, 657), (3, 438), (6, 219), (9, 146), (18, 73).
All these factor pairs result in 1314. 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 1314 by 1, 1314 ÷ 1 = 1314.
Step 2: Continue dividing 1314 by the numbers until the remainder becomes 0.
1314 ÷ 1 = 1314
1314 ÷ 2 = 657
1314 ÷ 3 = 438
1314 ÷ 6 = 219
1314 ÷ 9 = 146
1314 ÷ 18 = 73
Therefore, the factors of 1314 are: 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314.
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 1314 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1314 ÷ 2 = 657
657 ÷ 3 = 219
219 ÷ 3 = 73
73 ÷ 73 = 1
The prime factors of 1314 are 2, 3, and 73.
The prime factorization of 1314 is: 2 × 3 × 3 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1314 is divided by 2 to get 657.
Step 2: Now divide 657 by 3 to get 219.
Step 3: Then divide 219 by 3 to get 73.
Here, 73 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1314 is: 2 × 3 × 3 × 73.
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 1314: (1, 1314), (2, 657), (3, 438), (6, 219), (9, 146), and (18, 73).
Negative factor pairs of 1314: (-1, -1314), (-2, -657), (-3, -438), (-6, -219), (-9, -146), and (-18, -73).
Common Mistakes and How to Avoid Them in Factors of 1314
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 1314, 1 and 1314 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 1314 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1314/1.5 = 876, 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 1314 are prime numbers.
For example, 2, 3, and 73 are the prime factors of 1314, but it has other factors like 6 and 18.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1314 as 2 × 3 × 3 × 73 and missing all the key factors.
Factors of 1314 Examples
Problem 1
A farmer has 657 apples and wants to group them into baskets of 2 apples each. How many baskets can he fill?
He can fill 328 baskets.
Explanation
To divide the apples equally into baskets, we need to divide the total apples by the number of apples per basket. 657/2 = 328.5, rounding down since you can't have half a basket, gives us 328 baskets.
Problem 2
A rectangular garden has a length of 73 meters and a total area of 1314 square meters. Find the width.
18 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1314 = 73 × width
To find the value of width, we need to shift 73 to the left side.
1314/73 = width
Width = 18.
Problem 3
A teacher has 438 pencils and wants to distribute them equally among 3 classes. How many pencils will each class get?
Each class will get 146 pencils.
Explanation
To find the pencils in each class, divide the total pencils by the number of classes.
438/3 = 146
Problem 4
A concert has 219 seats divided into 6 equal sections. How many seats are there in each section?
There are 36 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
219/6 = 36.5, rounding down gives us 36 seats per section.
Problem 5
A baker has 1314 cookies and wants to arrange them in groups of 18. How many groups can be made?
73 groups can be made.
Explanation
Divide total cookies by the number of cookies per group.
1314/18 = 73
FAQs on Factors of 1314
1.What are the factors of 1314?
2.Mention the prime factors of 1314.
3.Is 1314 a multiple of 9?
4.Mention the factor pairs of 1314?
5.What is the square of 1314?
6.How can children in Philippines use numbers in everyday life to understand Factors of 1314?
7.What are some fun ways kids in Philippines can practice Factors of 1314 with numbers?
8.What role do numbers and Factors of 1314 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 1314 skills?
Important Glossaries for Factors of 1314
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, and 1314.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 73 are prime factors of 1314.
- 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 1314 are (1, 1314), (2, 657), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1314 is 2 × 3 × 3 × 73.
- Negative factors: Factors that are negative. For example, the negative factors of 1314 are -1, -2, -3, -6, -9, -18, -73, -146, -219, -438, -657, and -1314.
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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.
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