Last updated on May 26th, 2025
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 -65, how they are used in real life, and tips to learn them quickly.
The numbers that divide -65 evenly are known as factors of -65.
A factor of -65 is a number that divides the number without remainder.
The factors of -65 are 1, 5, 13, and 65.
Negative factors of -65: -1, -5, -13, and -65.
Prime factors of -65: 5 and 13.
Prime factorization of -65: -1 × 5 × 13.
The sum of positive factors of 65: 1 + 5 + 13 + 65 = 84
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 -65. Identifying the numbers which are multiplied to get -65 is the multiplication method.
Step 1: Multiply -65 by -1, -65 × -1 = 65.
Step 2: Check for other numbers that give -65 after multiplying
-1 × 65 = -65
-5 × 13 = -65
Therefore, the positive factor pairs of -65 are: (1, 65), (5, 13).
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 a simple division method
Step 1: Divide -65 by -1, -65 ÷ -1 = 65.
Step 2: Continue dividing -65 by the numbers until the remainder becomes 0.
-65 ÷ -1 = 65
-65 ÷ -5 = 13
-65 ÷ -13 = 5
-65 ÷ -65 = 1
Therefore, the factors of -65 are: 1, 5, 13, 65.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of -65 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-65 ÷ -1 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of -65 are 5 and 13.
The prime factorization of -65 is: -1 × 5 × 13.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -65 is divided by -1 to get 65.
Step 2: Now divide 65 by 5 to get 13. Step 3: 13 is a prime number and cannot be divided further.
So, the prime factorization of -65 is: -1 × 5 × 13.
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 -65: (1, 65), (5, 13).
Negative factor pairs of -65: (-1, -65), (-5, -13).
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 group has 13 students and a budget of $65. How much is allocated per student?
$5 is allocated per student.
To find the allocation per student, divide the total budget by the number of students.
65/13 = 5
A rectangular garden has a width of 5 meters and an area of 65 square meters. Find the length.
13 meters.
To find the length of the garden, we use the formula, Area = length × width 65 = 5 × length
To find the value of length, we need to shift 5 to the left side.
65/5 = length
Length = 13.
There are 5 baskets and 65 apples. How many apples are in each basket?
Each basket will have 13 apples.
To find the apples in each basket, divide the total apples by the baskets.
65/5 = 13
A concert venue has 65 seats and 13 rows. How many seats are there in each row?
There are 5 seats in each row.
Dividing the seats by the total rows, we will get the number of seats in each row.
65/13 = 5
A book collection has 65 books and 5 shelves. How many books will go on each shelf?
Each of the shelves has 13 books.
Divide total books by shelves.
65/5 = 13
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.