128 LearnersLast updated on May 26th, 2025
Factors of 1953
Factors are the numbers that divide a given number evenly without a 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 1953, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1953?
The numbers that divide 1953 evenly are known as factors of 1953.
A factor of 1953 is a number that divides the number without a remainder.
The factors of 1953 are 1, 3, 11, 33, 59, 177, 649, and 1953.
Negative factors of 1953: -1, -3, -11, -33, -59, -177, -649, and -1953.
Prime factors of 1953: 3, 11, and 59.
Prime factorization of 1953: 3 × 11 × 59.
The sum of factors of 1953: 1 + 3 + 11 + 33 + 59 + 177 + 649 + 1953 = 2886
How to Find Factors of 1953?
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 1953. Identifying the numbers which are multiplied to get the number 1953 is the multiplication method.
Step 1: Multiply 1953 by 1, 1953 × 1 = 1953.
Step 2: Check for other numbers that give 1953 after multiplying
3 × 651 = 1953
11 × 177 = 1953
33 × 59 = 1953
Therefore, the positive factor pairs of 1953 are: (1, 1953), (3, 651), (11, 177), (33, 59).
All these factor pairs result in 1953.
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 the simple division method
Step 1: Divide 1953 by 1, 1953 ÷ 1 = 1953.
Step 2: Continue dividing 1953 by the numbers until the remainder becomes 0.
1953 ÷ 1 = 1953
1953 ÷ 3 = 651
1953 ÷ 11 = 177
1953 ÷ 33 = 59
Therefore, the factors of 1953 are: 1, 3, 11, 33, 59, 177, 649, 1953.
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 1953 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1953 ÷ 3 = 651
651 ÷ 11 = 59
59 ÷ 59 = 1
The prime factors of 1953 are 3, 11, and 59.
The prime factorization of 1953 is: 3 × 11 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1953 is divided by 3 to get 651.
Step 2: Now divide 651 by 11 to get 59.
Step 3: Divide 59 by 59 to get 1. Here, 59 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1953 is: 3 × 11 × 59.
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 1953: (1, 1953), (3, 651), (11, 177), and (33, 59).
Negative factor pairs of 1953: (-1, -1953), (-3, -651), (-11, -177), and (-33, -59).
Common Mistakes and How to Avoid Them in Factors of 1953
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 1953, 1 and 1953 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 1953 consist of -1, -3, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 1953/1.5 = 1302, 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 1953 are prime numbers.
For example, 3, 11, and 59 are the prime factors of 1953, but it has other factors like 33, 177.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1953 as 3 × 11 × 59 and missing all the key factors.
Factors of 1953 Examples
Problem 1
There are 3 teams and 1953 participants. How will they distribute them equally?
They will have 651 participants each.
Explanation
To distribute the participants equally, we need to divide the total participants by the number of teams.
1953/3 = 651
Problem 2
A rectangular field has a length of 11 meters and a total area of 1953 square meters. What is the width?
177 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1953 = 11 × width
To find the value of width, we need to shift 11 to the left side.
1953/11 = width
Width = 177.
Problem 3
There are 33 trucks and 1953 boxes. How many boxes will be in each truck?
Each truck will have 59 boxes.
Explanation
To find the boxes in each truck, divide the total boxes by the trucks.
1953/33 = 59
Problem 4
In a class, there are 1953 students, and 59 groups. How many students are there in each group?
There are 33 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1953/59 = 33
Problem 5
1953 books need to be arranged on 177 shelves. How many books will go on each shelf?
Each of the shelves has 11 books.
Explanation
Divide total books by shelves.
1953/177 = 11
FAQs on Factors of 1953
1.What are the factors of 1953?
2.Mention the prime factors of 1953.
3.Is 1953 a multiple of 11?
4.Mention the factor pairs of 1953?
5.What is the square of 1953?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1953?
7.What are some fun ways kids in Qatar can practice Factors of 1953 with numbers?
8.What role do numbers and Factors of 1953 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1953 skills?
Important Glossaries for Factor of 1953
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1953 are 1, 3, 11, 33, 59, 177, 649, and 1953.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 59 are prime factors of 1953.
- 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 1953 are (1, 1953), (3, 651), etc.
- Prime factorization: Breaking down a number into its basic prime numbers. For example, the prime factorization of 1953 is 3 × 11 × 59.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 1953 is a multiple of 11.
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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.
