135 LearnersLast updated on May 26th, 2025
Factors of 960
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 960, how they are used in real life, and tips to learn them quickly.
What are the Factors of 960?
The numbers that divide 960 evenly are known as factors of 960.
A factor of 960 is a number that divides the number without remainder.
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960.
Negative factors of 960: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -160, -192, -240, -320, -480, and -960.
Prime factors of 960: 2, 3, and 5.
Prime factorization of 960: 26 × 3 × 5.
The sum of factors of 960: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 160 + 192 + 240 + 320 + 480 + 960 = 2976
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How to Find Factors of 960?
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 960. Identifying the numbers which are multiplied to get the number 960 is the multiplication method.
Step 1: Multiply 960 by 1, 960 × 1 = 960.
Step 2: Check for other numbers that give 960 after multiplying
2 × 480 = 960
3 × 320 = 960
4 × 240 = 960
5 × 192 = 960
6 × 160 = 960
8 × 120 = 960
10 × 96 = 960
12 × 80 = 960
15 × 64 = 960
16 × 60 = 960
20 × 48 = 960
24 × 40 = 960
30 × 32 = 960
Therefore, the positive factor pairs of 960 are: (1, 960), (2, 480), (3, 320), (4, 240), (5, 192), (6, 160), (8, 120), (10, 96), (12, 80), (15, 64), (16, 60), (20, 48), (24, 40), (30, 32).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 960 by 1, 960 ÷ 1 = 960.
Step 2: Continue dividing 960 by the numbers until the remainder becomes 0.
960 ÷ 1 = 960
960 ÷ 2 = 480
960 ÷ 3 = 320
960 ÷ 4 = 240
960 ÷ 5 = 192
960 ÷ 6 = 160
960 ÷ 8 = 120
960 ÷ 10 = 96
960 ÷ 12 = 80
960 ÷ 15 = 64
960 ÷ 16 = 60
960 ÷ 20 = 48
960 ÷ 24 = 40
960 ÷ 30 = 32
Therefore, the factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 960 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
960 ÷ 2 = 480
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 960 are 2, 3, and 5. The prime factorization of 960 is: 26 × 3 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 960 is divided by 2 to get 480.
Step 2: Now divide 480 by 2 to get 240.
Step 3: Then divide 240 by 2 to get 120.
Step 4: Divide 120 by 2 to get 60.
Step 5: Divide 60 by 2 to get 30.
Step 6: Divide 30 by 2 to get 15.
Step 7: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 960 is: 26 × 3 × 5.
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 960: (1, 960), (2, 480), (3, 320), (4, 240), (5, 192), (6, 160), (8, 120), (10, 96), (12, 80), (15, 64), (16, 60), (20, 48), (24, 40), (30, 32).
Negative factor pairs of 960: (-1, -960), (-2, -480), (-3, -320), (-4, -240), (-5, -192), (-6, -160), (-8, -120), (-10, -96), (-12, -80), (-15, -64), (-16, -60), (-20, -48), (-24, -40), (-30, -32).
Common Mistakes and How to Avoid Them in Factors of 960
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 960, 1 and 960 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 960 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 960/1.5 = 640, 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 960 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 960, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 960 as 2^6 × 3 × 5 and missing all the key factors.
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Factors of 960 Examples
Problem 1
A team has 10 members and 960 candies. How will they divide it equally?
They will get 96 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of team members.
960/10 = 96
Problem 2
A rectangular garden has a length of 20 meters and a total area of 960 square meters. Find the width.
48 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width 960 = 20 × width
To find the value of width, we need to shift 20 to the left side.
960/20 = width
Width = 48.
Problem 3
There are 16 boxes and 960 marbles. How many marbles will be in each box?
Each box will have 60 marbles.
Explanation
To find the number of marbles in each box, divide the total number of marbles by the boxes.
960/16 = 60
Problem 4
In a school, there are 960 students, and 15 classes. How many students are there in each class?
There are 64 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
960/15 = 64
Problem 5
960 books need to be arranged in 6 bookshelves. How many books will go on each shelf?
Each of the bookshelves has 160 books.
Explanation
Divide total books by bookshelves.
960/6 = 160
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FAQs on Factors of 960
1.What are the factors of 960?
2.Mention the prime factors of 960.
3.Is 960 a multiple of 8?
4.Mention the factor pairs of 960?
5.What is the square of 960?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 960?
7.What are some fun ways kids in Vietnam can practice Factors of 960 with numbers?
8.What role do numbers and Factors of 960 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 960 skills?
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Important Glossaries for Factor of 960
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 960 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 960.
- 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 960 are (1, 960), (2, 480), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 960 is 2^6 × 3 × 5.
- Multiples: A number is a multiple of its factors. For example, 960 is a multiple of 8.
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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.
