139 LearnersLast updated on May 28th, 2025
Factors of 1307
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 1307, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1307?
The numbers that divide 1307 evenly are known as factors of 1307.
A factor of 1307 is a number that divides the number without remainder.
The factors of 1307 are 1, 19, 67, and 1307.
Negative factors of 1307: -1, -19, -67, and -1307.
Prime factors of 1307: 19 and 67.
Prime factorization of 1307: 19 × 67.
The sum of factors of 1307: 1 + 19 + 67 + 1307 = 1394
How to Find Factors of 1307?
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 1307. Identifying the numbers which are multiplied to get the number 1307 is the multiplication method.
Step 1: Multiply 1307 by 1, 1307 × 1 = 1307.
Step 2: Check for other numbers that give 1307 after multiplying
19 × 67 = 1307
Therefore, the positive factor pairs of 1307 are: (1, 1307) and (19, 67).
All these factor pairs result in 1307.
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 1307 by 1, 1307 ÷ 1 = 1307.
Step 2: Continue dividing 1307 by the numbers until the remainder becomes 0.
1307 ÷ 1 = 1307
1307 ÷ 19 = 67
Therefore, the factors of 1307 are: 1, 19, 67, 1307.
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 1307 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1307 ÷ 19 = 67
67 ÷ 67 = 1
The prime factors of 1307 are 19 and 67.
The prime factorization of 1307 is: 19 × 67.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1307 is divided by 19 to get 67.
Step 2: Now divide 67 by 67 to get 1.
Here, 67 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1307 is: 19 × 67.
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 1307: (1, 1307) and (19, 67).
Negative factor pairs of 1307: (-1, -1307) and (-19, -67).
Common Mistakes and How to Avoid Them in Factors of 1307
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1307, 1 and 1307 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 1307 consist of -1, -19, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1307/1.5 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 1307 are prime numbers.
For example, 19 and 67 are the prime factors of 1307, but it has other factors like 1, 1307.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1307 as 19 × 67 and missing all the key factors.
Factors of 1307 Examples
Problem 1
There are 19 teams in a tournament and 1307 players. How will they distribute players equally among the teams?
Each team will have 67 players.
Explanation
To distribute the players equally, we need to divide the total players by the number of teams.
1307/19 = 67
Problem 2
A rectangular garden has a width of 19 meters and a total area of 1307 square meters. Find the length.
The length is 67 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1307 = length × 19
To find the value of length, we need to shift 19 to the left side.
1307/19 = length
Length = 67.
Problem 3
A library has 1307 books and 67 sections. How many books will be in each section?
Each section will have 19 books.
Explanation
To find the books in each section, divide the total books by the sections.
1307/67 = 19
Problem 4
In a workshop, there are 1307 tools, and 19 boxes. How many tools are there in each box?
There are 67 tools in each box.
Explanation
Dividing the tools by the total boxes, we will get the number of tools in each box.
1307/19 = 67
Problem 5
1307 apples need to be packed in 67 crates. How many apples will go into each crate?
Each crate will have 19 apples.
Explanation
Divide the total apples by the crates.
1307/67 = 19
FAQs on Factors of 1307
1.What are the factors of 1307?
2.Mention the prime factors of 1307.
3.Is 1307 a multiple of 19?
4.Mention the factor pairs of 1307?
5.What is the square of 1307?
6.How can children in Philippines use numbers in everyday life to understand Factors of 1307?
7.What are some fun ways kids in Philippines can practice Factors of 1307 with numbers?
8.What role do numbers and Factors of 1307 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 1307 skills?
Important Glossaries for Factor of 1307
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1307 are 1, 19, 67, and 1307.
- Prime factors: The factors which are prime numbers. For example, 19 and 67 are prime factors of 1307.
- 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 1307 are (1, 1307) and (19, 67).
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1307 is 19 × 67.
- Multiples: A number is a multiple of its factors. For example, 1307 is a multiple of 19 and 67.
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About BrightChamps in Philippines
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.
