118 LearnersLast updated on May 26th, 2025
Factors of -65
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.
What are the Factors of -65?
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
How to Find Factors of -65?
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 -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.
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 -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.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 -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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of -65
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 -65, 1 and 65 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 -65 consist of -1, -5, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as fractions. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -65/1.5 = -43.333, 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 -65 are prime numbers.
For example, 5 and 13 are the prime factors of -65, but it has other factors like 1, 65.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -65 as -1 × 5 × 13 and missing all the key factors.
Factors of -65 Examples
Problem 1
A group has 13 students and a budget of $65. How much is allocated per student?
$5 is allocated per student.
Explanation
To find the allocation per student, divide the total budget by the number of students.
65/13 = 5
Problem 2
A rectangular garden has a width of 5 meters and an area of 65 square meters. Find the length.
13 meters.
Explanation
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.
Problem 3
There are 5 baskets and 65 apples. How many apples are in each basket?
Each basket will have 13 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
65/5 = 13
Problem 4
A concert venue has 65 seats and 13 rows. How many seats are there in each row?
There are 5 seats in each row.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
65/13 = 5
Problem 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.
Explanation
Divide total books by shelves.
65/5 = 13
FAQs on Factors of -65
1.What are the factors of -65?
2.Mention the prime factors of -65.
3.Is 65 a multiple of 5?
4.Mention the factor pairs of -65?
5.What is the square of 65?
6.How can children in Qatar use numbers in everyday life to understand Factors of -65?
7.What are some fun ways kids in Qatar can practice Factors of -65 with numbers?
8.What role do numbers and Factors of -65 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -65 skills?
Important Glossaries for Factors of -65
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -65 are 1, 5, 13, and 65.
- Prime factors: The factors which are prime numbers. For example, 5 and 13 are prime factors of -65.
- 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 -65 are (1, 65), (5, 13), etc.
- Negative factors: Factors that are negative numbers dividing the original number without remainder. For example, the negative factors of -65 are -1, -5, -13, and -65.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of -65 is -1 × 5 × 13.
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About BrightChamps in Qatar
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.
