120 LearnersLast updated on May 26th, 2025
Factors of 767
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 767, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 767?
The numbers that divide 767 evenly are known as factors of 767.
A factor of 767 is a number that divides the number without remainder.
The factors of 767 are 1, 13, 59, and 767. \
Negative factors of 767: -1, -13, -59, and -767.
Prime factors of 767: 13 and 59.
Prime factorization of 767: 13 × 59.
The sum of factors of 767: 1 + 13 + 59 + 767 = 840
How to Find Factors of 767?
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 767. Identifying the numbers which are multiplied to get the number 767 is the multiplication method.
Step 1: Multiply 767 by 1, 767 × 1 = 767.
Step 2: Check for other numbers that give 767 after multiplying
13 × 59 = 767
Therefore, the positive factor pairs of 767 are: (1, 767), (13, 59). All these factor pairs result in 767.
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 767 by 1, 767 ÷ 1 = 767.
Step 2: Continue dividing 767 by the numbers until the remainder becomes 0.
767 ÷ 1 = 767
767 ÷ 13 = 59
Therefore, the factors of 767 are: 1, 13, 59, 767.
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 767 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
767 ÷ 13 = 59
59 ÷ 59 = 1
The prime factors of 767 are 13 and 59.
The prime factorization of 767 is: 13 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 767 is divided by 13 to get 59.
Step 2: Now divide 59 by 59 to get 1. Here, 59 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 767 is: 13 × 59.
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 767: (1, 767), (13, 59).
Negative factor pairs of 767: (-1, -767), (-13, -59).
Common Mistakes and How to Avoid Them in Factors of 767
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 767, 1 and 767 is also a factor.
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 767 consist of -1, -13, -59, etc.
Mistake 3
Including the Fraction
Children might sometimes add fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 767/1.5 = 511.333, 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 767 are prime numbers.
For example, 13 and 59 are the prime factors of 767, but it has other factors like 1 and 767.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 767 as 13 × 59 and missing all the key factors.
Factors of 767 Examples
Problem 1
There are 767 pages to be equally distributed among 13 editors. How many pages will each editor receive?
Each editor will receive 59 pages.
Explanation
To distribute the pages equally, we need to divide the total pages by the number of editors.
767/13 = 59
Problem 2
A rectangular garden is 13 meters in one dimension, with a total area of 767 square meters. What is the length of the other dimension?
59 meters.
Explanation
To find the other dimension of the garden, we use the formula,
Area = length × width
767 = 13 × width
To find the value of width, we need to shift 13 to the left side.
767/13 = width
Width = 59.
Problem 3
There are 59 students and 767 pencils. How many pencils will each student receive?
Each student will receive 13 pencils.
Explanation
To find the pencils each student receives, divide the total pencils by the students.
767/59 = 13
Problem 4
In a library, 767 books need to be arranged on 13 shelves. How many books will go on each shelf?
Each shelf will have 59 books.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
767/13 = 59
Problem 5
A school has 767 students and 59 buses. How many students should be on each bus?
Each bus should have 13 students.
Explanation
Divide the total students by the buses.
767/59 = 13
FAQs on Factors of 767
1.What are the factors of 767?
2.Mention the prime factors of 767.
3.Is 767 a multiple of 13?
4.Mention the factor pairs of 767?
5.What is the square of 767?
Important Glossaries for Factors of 767
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 767 are 1, 13, 59, and 767.
- Prime factors: The factors which are prime numbers. For example, 13 and 59 are prime factors of 767.
- 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 767 are (1, 767) and (13, 59).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 767 is 13 × 59.
- Negative factors: Factors that are negative counterparts of the positive factors. For example, the negative factors of 767 are -1, -13, -59, and -767.
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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.
