117 LearnersLast updated on May 26th, 2025
Factors of 1968
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 1968, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1968?
The numbers that divide 1968 evenly are known as factors of 1968.
A factor of 1968 is a number that divides the number without remainder.
The factors of 1968 are 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, and 1968.
Negative factors of 1968: -1, -2, -3, -4, -6, -12, -164, -246, -328, -492, -656, -984, and -1968.
Prime factors of 1968: 2 and 3.
Prime factorization of 1968: 23 × 3 × 41.
The sum of factors of 1968: 1 + 2 + 3 + 4 + 6 + 12 + 164 + 246 + 328 + 492 + 656 + 984 + 1968 = 4866
How to Find Factors of 1968?
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 1968. Identifying the numbers which are multiplied to get the number 1968 is the multiplication method.
Step 1: Multiply 1968 by 1, 1968 × 1 = 1968.
Step 2: Check for other numbers that give 1968 after multiplying
2 × 984 = 1968
3 × 656 = 1968
4 × 492 = 1968
6 × 328 = 1968
12 × 164 = 1968
Therefore, the positive factor pairs of 1968 are: (1, 1968), (2, 984), (3, 656), (4, 492), (6, 328), (12, 164).
All these factor pairs result in 1968.
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 1968 by 1, 1968 ÷ 1 = 1968.
Step 2: Continue dividing 1968 by the numbers until the remainder becomes 0.
1968 ÷ 1 = 1968
1968 ÷ 2 = 984
1968 ÷ 3 = 656
1968 ÷ 4 = 492
1968 ÷ 6 = 328
1968 ÷ 12 = 164
Therefore, the factors of 1968 are: 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, 1968.
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 1968 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1968 ÷ 2 = 984
984 ÷ 2 = 492
492 ÷ 2 = 246
246 ÷ 3 = 82
82 ÷ 41 = 2
41 ÷ 41 = 1
The prime factors of 1968 are 2, 3, and 41.
The prime factorization of 1968 is: 23 × 3 × 41.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1968 is divided by 2 to get 984.
Step 2: Now divide 984 by 2 to get 492.
Step 3: Then divide 492 by 2 to get 246.
Step 4: Divide 246 by 3 to get 82.
Step 5: Divide 82 by 41 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1968 is: 23 × 3 × 41.
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 1968: (1, 1968), (2, 984), (3, 656), (4, 492), (6, 328), (12, 164).
Negative factor pairs of 1968: (-1, -1968), (-2, -984), (-3, -656), (-4, -492), (-6, -328), (-12, -164).
Common Mistakes and How to Avoid Them in Factors of 1968
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 1968, 1 and 1968 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 1968 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1968/1.5 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 1968 are prime numbers.
For example, 2, 3, and 41 are the prime factors of 1968, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1968 as 2^3 × 3 × 41 and missing all the key factors.
Factors of 1968 Examples
Problem 1
There are 12 friends and 1968 candies. How will they divide it equally?
They will get 164 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1968/12 = 164
Problem 2
A field is rectangular, the length of the field is 41 meters and the total area is 1968 square meters. Find the width?
48 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1968 = 41 × width
To find the value of width, we need to shift 41 to the left side.
1968/41 = width
Width = 48.
Problem 3
There are 6 bags and 1968 cookies. How many cookies will be in each bag?
Each bag will have 328 cookies.
Explanation
To find the cookies in each bag, divide the total cookies with the bags.
1968/6 = 328
Problem 4
In a class, there are 1968 students, and 12 groups. How many students are there in each group?
There are 164 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1968/12 = 164
Problem 5
1968 books need to be arranged in 164 shelves. How many books will go on each shelf?
Each of the shelves has 12 books.
Explanation
Divide total books with shelves.
1968/164 = 12
FAQs on Factors of 1968
1.What are the factors of 1968?
2.Mention the prime factors of 1968.
3.Is 1968 a multiple of 6?
4.Mention the factor pairs of 1968?
5.What is the square of 1968?
Important Glossaries for Factor of 1968
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1968 are 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, and 1968.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 41 are prime factors of 1968.
- 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 1968 are (1, 1968), (2, 984), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1968 is 23 × 3 × 41.
- Multiple: A number that can be divided by another number without a remainder. For example, 1968 is a multiple of 6.
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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.
