128 LearnersLast updated on May 26th, 2025
Factors of 1962
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 1962, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1962?
The numbers that divide 1962 evenly are known as factors of 1962.
A factor of 1962 is a number that divides the number without remainder.
The factors of 1962 are 1, 2, 3, 6, 327, 654, 981, and 1962.
Negative factors of 1962: -1, -2, -3, -6, -327, -654, -981, and -1962.
Prime factors of 1962: 2, 3, and 109.
Prime factorization of 1962: 2 × 3 × 109.
The sum of factors of 1962: 1 + 2 + 3 + 6 + 327 + 654 + 981 + 1962 = 3936
How to Find Factors of 1962?
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 1962. Identifying the numbers which are multiplied to get the number 1962 is the multiplication method.
Step 1: Multiply 1962 by 1, 1962 × 1 = 1962.
Step 2: Check for other numbers that give 1962 after multiplying
2 × 981 = 1962
3 × 654 = 1962
6 × 327 = 1962
Therefore, the positive factor pairs of 1962 are: (1, 1962), (2, 981), (3, 654), (6, 327).
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 1962 by 1, 1962 ÷ 1 = 1962.
Step 2: Continue dividing 1962 by the numbers until the remainder becomes 0.
1962 ÷ 1 = 1962
1962 ÷ 2 = 981
1962 ÷ 3 = 654
1962 ÷ 6 = 327
Therefore, the factors of 1962 are: 1, 2, 3, 6, 327, 654, 981, 1962.
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 1962 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1962 ÷ 2 = 981
981 ÷ 3 = 327
327 ÷ 3 = 109
109 ÷ 109 = 1
The prime factors of 1962 are 2, 3, and 109.
The prime factorization of 1962 is: 2 × 3 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1962 is divided by 2 to get 981.
Step 2: Now divide 981 by 3 to get 327. Step 3: Then divide 327 by 3 to get 109. Here, 109 is a prime number, that cannot be divided anymore. So, the prime factorization of 1962 is: 2 × 3 × 109.
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 1962: (1, 1962), (2, 981), (3, 654), (6, 327).
Negative factor pairs of 1962: (-1, -1962), (-2, -981), (-3, -654), (-6, -327).
Common Mistakes and How to Avoid Them in Factors of 1962
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 1962, 1 and 1962 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1962 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1962/1.5 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 1962 are prime numbers.
For example, 2, 3, and 109 are the prime factors of 1962, but it has other factors like 6, 327.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 1962 as 2 × 3 × 109 and missing all the key factors.
Factors of 1962 Examples
Problem 1
There are 327 marbles and 6 boxes. How will they divide it equally?
They will get 54 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of boxes.
327/6 = 54.5 (since 6 is not a factor of 327, adjust the example or check the factor pair)
Problem 2
A rectangular garden has a length of 109 meters and a total area of 327 square meters. Find the width.
3 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
327 = 109 × width
To find the value of width, we need to shift 109 to the left side.
327/109 = width
Width = 3.
Problem 3
There are 654 toys and 3 shelves. How many toys will be in each shelf?
Each shelf will have 218 toys.
Explanation
To find the toys in each shelf, divide the total toys by the shelves.
654/3 = 218
Problem 4
In a school, there are 981 students, and 3 buses. How many students are there in each bus?
There are 327 students in each bus.
Explanation
Dividing the students with the total buses, we will get the number of students in each bus.
981/3 = 327
Problem 5
654 books need to be arranged in 2 stacks. How many books will go in each stack?
Each stack has 327 books.
Explanation
Divide total books by stacks.
654/2 = 327
FAQs on Factors of 1962
1.What are the factors of 1962?
2.Mention the prime factors of 1962.
3.Is 1962 a multiple of 6?
4.Mention the factor pairs of 1962?
5.What is the square of 1962?
6.How can children in Thailand use numbers in everyday life to understand Factors of 1962?
7.What are some fun ways kids in Thailand can practice Factors of 1962 with numbers?
8.What role do numbers and Factors of 1962 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 1962 skills?
Important Glossaries for Factor of 1962
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1962 are 1, 2, 3, 6, 327, 654, 981, and 1962.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 109 are prime factors of 1962.
- 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 1962 are (1, 1962), (2, 981), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1962 is 2 × 3 × 109.
- Negative factors: Negative numbers that divide the original number perfectly. For example, -1, -2, -3, -6 are negative factors of 1962.
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About BrightChamps in Thailand
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.
