121 LearnersLast updated on May 26th, 2025
Factors of 1956
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 1956, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1956?
The numbers that divide 1956 evenly are known as factors of 1956.
A factor of 1956 is a number that divides the number without remainder.
The factors of 1956 are 1, 2, 3, 4, 6, 12, 163, 326, 489, 652, 978, and 1956.
Negative factors of 1956: -1, -2, -3, -4, -6, -12, -163, -326, -489, -652, -978, and -1956.
Prime factors of 1956: 2, 3, and 163.
Prime factorization of 1956: 2 × 2 × 3 × 163.
The sum of factors of 1956: 1 + 2 + 3 + 4 + 6 + 12 + 163 + 326 + 489 + 652 + 978 + 1956 = 4592
How to Find Factors of 1956?
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 1956. Identifying the numbers which are multiplied to get the number 1956 is the multiplication method.
Step 1: Multiply 1956 by 1, 1956 × 1 = 1956.
Step 2: Check for other numbers that give 1956 after multiplying
2 × 978 = 1956
3 × 652 = 1956
4 × 489 = 1956
6 × 326 = 1956
12 × 163 = 1956
Therefore, the positive factor pairs of 1956 are: (1, 1956), (2, 978), (3, 652), (4, 489), (6, 326), (12, 163).
All these factor pairs result in 1956. 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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 1956 by 1, 1956 ÷ 1 = 1956.
Step 2: Continue dividing 1956 by the numbers until the remainder becomes 0.
1956 ÷ 1 = 1956
1956 ÷ 2 = 978
1956 ÷ 3 = 652
1956 ÷ 4 = 489
1956 ÷ 6 = 326
1956 ÷ 12 = 163
Therefore, the factors of 1956 are: 1, 2, 3, 4, 6, 12, 163, 326, 489, 652, 978, 1956.
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 1956 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1956 ÷ 2 = 978
978 ÷ 2 = 489
489 ÷ 3 = 163
163 ÷ 163 = 1
The prime factors of 1956 are 2, 3, and 163.
The prime factorization of 1956 is: 2 × 2 × 3 × 163.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1956 is divided by 2 to get 978.
Step 2: Now divide 978 by 2 to get 489.
Step 3: Then divide 489 by 3 to get 163. Step 4: Here, 163 is a prime number that cannot be divided anymore. So, the prime factorization of 1956 is: 2 × 2 × 3 × 163.
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 1956: (1, 1956), (2, 978), (3, 652), (4, 489), (6, 326), (12, 163).
Negative factor pairs of 1956: (-1, -1956), (-2, -978), (-3, -652), (-4, -489), (-6, -326), (-12, -163).
Common Mistakes and How to Avoid Them in Factors of 1956
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 1956, 1 and 1956 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 1956 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1956/1.5 = 1304, 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 1956 are prime numbers.
For example, 2, 3, and 163 are the prime factors of 1956, but it has other factors like 4, 6.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1956 as 2 × 2 × 3 × 163 and missing all the key factors.
Factors of 1956 Examples
Problem 1
There are 6 groups and 1956 items. How will they divide it equally?
They will get 326 items each.
Explanation
To divide the items equally, we need to divide the total items by the number of groups.
1956/6 = 326
Problem 2
A rectangular garden has a width of 4 meters and a total area of 1956 square meters. Find the length.
489 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1956 = length × 4
To find the value of the length, we need to shift 4 to the left side.
1956/4 = length
Length = 489.
Problem 3
There are 12 baskets and 1956 apples. How many apples will be in each basket?
Each basket will have 163 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1956/12 = 163
Problem 4
In a stadium, there are 163 rows and 1956 seats. How many seats are there in each row?
There are 12 seats in each row.
Explanation
Dividing the seats by the total number of rows, we will get the number of seats in each row.
1956/163 = 12
Problem 5
1956 units of material need to be stored in 3 warehouses. How many units will go in each warehouse?
Each of the warehouses has 652 units.
Explanation
Divide total units by the number of warehouses.
1956/3 = 652
FAQs on Factors of 1956
1.What are the factors of 1956?
2.Mention the prime factors of 1956.
3.Is 1956 a multiple of 4?
4.Mention the factor pairs of 1956?
5.What is the square of 1956?
Important Glossaries for Factors of 1956
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1956 are 1, 2, 3, 4, 6, 12, 163, 326, 489, 652, 978, and 1956.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 163 are prime factors of 1956.
- 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 1956 are (1, 1956), (2, 978), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1956 is 2 × 2 × 3 × 163.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 1956 is a multiple of 4.
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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.
