136 LearnersLast updated on May 26th, 2025
Factors of 965
Factors are the numbers that divide any given number evenly without a 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 965, how they are used in real life, and tips to learn them quickly.
What are the Factors of 965?
The numbers that divide 965 evenly are known as factors of 965.
A factor of 965 is a number that divides the number without a remainder.
The factors of 965 are 1, 5, 193, and 965.
Negative factors of 965: -1, -5, -193, and -965.
Prime factors of 965: 5 and 193.
Prime factorization of 965: 5 × 193.
The sum of factors of 965: 1 + 5 + 193 + 965 = 1164
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How to Find Factors of 965?
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 965. Identifying the numbers that are multiplied to get the number 965 is the multiplication method.
Step 1: Multiply 965 by 1, 965 × 1 = 965.
Step 2: Check for other numbers that give 965 after multiplying
5 × 193 = 965
Therefore, the positive factor pairs of 965 are: (1, 965) and (5, 193).
All these factor pairs result in 965.
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 the simple division method -
Step 1: Divide 965 by 1, 965 ÷ 1 = 965.
Step 2: Continue dividing 965 by the numbers until the remainder becomes 0.
965 ÷ 1 = 965
965 ÷ 5 = 193
Therefore, the factors of 965 are: 1, 5, 193, and 965.
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 965 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
965 ÷ 5 = 193
193 ÷ 193 = 1
The prime factors of 965 are 5 and 193
The prime factorization of 965 is: 5 × 193.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 965 is divided by 5 to get 193.
Step 2: 193 is a prime number and cannot be divided further. So, the prime factorization of 965 is: 5 × 193.
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 965: (1, 965) and (5, 193).
Negative factor pairs of 965: (-1, -965) and (-5, -193).
Common Mistakes and How to Avoid Them in Factors of 965
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 965, 1 and 965 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 965 consist of -1, -5, -193, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor because 965/2.5 = 386, but it is not a whole division.
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 965 are prime numbers.
For example, 5 and 193 are the prime factors of 965, but it has other factors like 1, 965.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 965 as 5 × 193 and missing all the key factors.
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Factors of 965 Examples
Problem 1
A teacher has 965 books and wants to distribute them equally among 5 classrooms. How many books will each classroom receive?
Each classroom will receive 193 books.
Explanation
To distribute the books equally, we need to divide the total number of books by the number of classrooms.
965/5 = 193
Problem 2
A rectangular garden has a length of 193 meters and a total area of 965 square meters. Find the width of the garden.
5 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
965 = 193 × width
To find the value of width, we need to shift 193 to the left side.
965/193 = width
Width = 5.
Problem 3
There are 5 friends planning to share 965 marbles equally. How many marbles will each friend get?
Each friend will get 193 marbles.
Explanation
To find the marbles each friend gets, divide the total marbles by the number of friends.
965/5 = 193
Problem 4
A conference room has 965 seats and 5 sections. How many seats are there in each section?
There are 193 seats in each section.
Explanation
Dividing the total number of seats by the number of sections gives the number of seats in each section.
965/5 = 193
Problem 5
A baker has 965 cookies and wants to pack them into boxes of 193. How many boxes will he need?
He will need 5 boxes.
Explanation
Divide the total cookies by the number of cookies per box.
965/193 = 5
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FAQs on Factors of 965
1.What are the factors of 965?
2.Mention the prime factors of 965.
3.Is 965 a multiple of 5?
4.Mention the factor pairs of 965.
5.What is the square of 965?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 965?
7.What are some fun ways kids in Vietnam can practice Factors of 965 with numbers?
8.What role do numbers and Factors of 965 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 965 skills?
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Important Glossaries for Factor of 965
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 965 are 1, 5, 193, and 965.
- Prime factors: The factors which are prime numbers. For example, 5 and 193 are prime factors of 965.
- 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 965 are (1, 965) and (5, 193).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 965 is 5 × 193.
- Division method: A method to find factors by dividing the number by integers, checking for zero remainders.
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About BrightChamps in Vietnam
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.
