Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To distribute the books equally, we need to divide the total number of books by the number of classrooms.
965/5 = 193
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.
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.
There are 5 friends planning to share 965 marbles equally. How many marbles will each friend get?
Each friend will get 193 marbles.
To find the marbles each friend gets, divide the total marbles by the number of friends.
965/5 = 193
A conference room has 965 seats and 5 sections. How many seats are there in each section?
There are 193 seats in each section.
Dividing the total number of seats by the number of sections gives the number of seats in each section.
965/5 = 193
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.
Divide the total cookies by the number of cookies per box.
965/193 = 5
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.
: She loves to read number jokes and games.