127 LearnersLast updated on May 26th, 2025
Factors of 1957
Factors are the numbers that divide any 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 1957, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1957?
The numbers that divide 1957 evenly are known as factors of 1957.
A factor of 1957 is a number that divides the number without a remainder.
The factors of 1957 are 1, 37, 53, and 1957.
Negative factors of 1957: -1, -37, -53, and -1957.
Prime factors of 1957: 37 and 53.
Prime factorization of 1957: 37 × 53.
The sum of factors of 1957: 1 + 37 + 53 + 1957 = 2048
How to Find Factors of 1957?
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 1957. Identifying the numbers which are multiplied to get the number 1957 is the multiplication method.
Step 1: Multiply 1957 by 1, 1957 × 1 = 1957.
Step 2: Check for other numbers that give 1957 after multiplying:
37 × 53 = 1957
Therefore, the positive factor pairs of 1957 are: (1, 1957) and (37, 53). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 1957 by 1, 1957 ÷ 1 = 1957.
Step 2: Continue dividing 1957 by the numbers until the remainder becomes 0.
1957 ÷ 1 = 1957
1957 ÷ 37 = 53
1957 ÷ 53 = 37
Therefore, the factors of 1957 are: 1, 37, 53, and 1957.
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 1957 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1957 ÷ 37 = 53
53 ÷ 53 = 1
The prime factors of 1957 are 37 and 53.
The prime factorization of 1957 is: 37 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1957 is divided by 37 to get 53.
Step 2: 53 is a prime number and cannot be divided further. So, the prime factorization of 1957 is: 37 × 53.
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 1957: (1, 1957) and (37, 53).
Negative factor pairs of 1957: (-1, -1957) and (-37, -53).
Common Mistakes and How to Avoid Them in Factors of 1957
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1957, 1 and 1957 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 1957 consist of -1, -37, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1957/1.5 = 1304.666..., 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 1957 are prime numbers.
For example, 37 and 53 are the prime factors of 1957, but it has other factors like 1 and 1957.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1957 as 37 × 53 and missing key factors.
Factors of 1957 Examples
Problem 1
A library has 1957 books and wants to arrange them equally on 37 shelves. How many books will each shelf have?
Each shelf will have 53 books.
Explanation
To arrange the books equally, divide the total books by the number of shelves.
1957/37 = 53
Problem 2
A rectangular garden has an area of 1957 square meters and a width of 53 meters. What is the length of the garden?
37 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1957 = length × 53
To find the value of length, we need to divide 1957 by 53.
1957/53 = length
Length = 37.
Problem 3
A concert hall is selling tickets and has 1957 seats available. If each row has 53 seats, how many rows are there?
There are 37 rows.
Explanation
To find the number of rows, divide the total number of seats by the number of seats per row.
1957/53 = 37
Problem 4
A company packs 1957 products in boxes, with each box containing 37 products. How many boxes are needed?
53 boxes are needed.
Explanation
Dividing the total number of products by the number of products per box, we will get the number of boxes needed.
1957/37 = 53
Problem 5
A total of 1957 flyers need to be distributed equally among 53 volunteers. How many flyers will each volunteer distribute?
Each volunteer will distribute 37 flyers.
Explanation
Divide the total flyers by the volunteers.
1957/53 = 37
FAQs on Factors of 1957
1.What are the factors of 1957?
2.Mention the prime factors of 1957.
3.Is 1957 a multiple of 37?
4.Mention the factor pairs of 1957?
5.What is the square of 1957?
Important Glossaries for Factor of 1957
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1957 are 1, 37, 53, and 1957.
- Prime factors: The factors which are prime numbers. For example, 37 and 53 are prime factors of 1957.
- 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 1957 are (1, 1957) and (37, 53).
- Prime factorization: The expression of a number as the product of its prime factors. For example, 1957 is expressed as 37 × 53.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1957 is a multiple of 37.
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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.
