126 LearnersLast updated on May 26th, 2025
Factors of 1057
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 1057, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1057?
The numbers that divide 1057 evenly are known as factors of 1057.
A factor of 1057 is a number that divides the number without remainder.
The factors of 1057 are 1, 7, 151, and 1057.
Negative factors of 1057: -1, -7, -151, and -1057.
Prime factors of 1057: 7 and 151
Prime factorization of 1057: 7 × 151.
The sum of factors of 1057: 1 + 7 + 151 + 1057 = 1216
How to Find Factors of 1057?
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 1057. Identifying the numbers which are multiplied to get the number 1057 is the multiplication method.
Step 1: Multiply 1057 by 1, 1057 × 1 = 1057.
Step 2: Check for other numbers that give 1057 after multiplying 7 × 151 = 1057
Therefore, the positive factor pairs of 1057 are: (1, 1057) and (7, 151). All these factor pairs result in 1057. 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 1057 by 1, 1057 ÷ 1 = 1057.
Step 2: Continue dividing 1057 by the numbers until the remainder becomes 0.
1057 ÷ 1 = 1057
1057 ÷ 7 = 151
Therefore, the factors of 1057 are: 1, 7, 151, 1057.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1057 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1057 ÷ 7 = 151
151 ÷ 151 = 1
The prime factors of 1057 are 7 and 151.
The prime factorization of 1057 is: 7 × 151.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1057 is divided by 7 to get 151.
Step 2: Now divide 151 by 151 to get 1. Here, 151 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1057 is: 7 × 151.
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 1057: (1, 1057) and (7, 151).
Negative factor pairs of 1057: (-1, -1057) and (-7, -151).
Common Mistakes and How to Avoid Them in Factors of 1057
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1057, 1 and 1057 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 1057 consist of -1, -7, 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 1057/1.5 = 704.666, 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 1057 are prime numbers.
For example, 7 and 151 are the prime factors of 1057, but it has other factors like 1, 1057.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1057 as 7 × 151 and missing all the key factors.
Factors of 1057 Examples
Problem 1
There are 7 teams and 1057 players. How will they distribute them equally?
They will get 151 players each.
Explanation
To distribute the players equally, we need to divide the total players by the number of teams.
1057/7 = 151
Problem 2
A bookshelf is rectangular, the height of the bookshelf is 151 cm and the total area is 1057 square cm. Find the width?
7 cm.
Explanation
To find the width of the bookshelf, we use the formula,
Area = height × width
1057 = 151 × width
To find the value of width, we need to shift 151 to the left side.
1057/151 = width
Width = 7.
Problem 3
There are 151 sections and 1057 books. How many books will be in each section?
Each section will have 7 books.
Explanation
To find the books in each section, divide the total books by the sections.
1057/151 = 7
Problem 4
In a tournament, there are 1057 participants, and 151 groups. How many participants are there in each group?
There are 7 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group. 1057/151 = 7
Problem 5
1057 seats need to be arranged in 7 rows. How many seats will go in each row?
Each of the rows has 151 seats.
Explanation
Divide total seats by rows. 1057/7 = 151
FAQs on Factors of 1057
1.What are the factors of 1057?
2.Mention the prime factors of 1057.
3.Is 1057 a multiple of 7?
4.Mention the factor pairs of 1057?
5.What is the square of 1057?
Important Glossaries for Factors of 1057
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1057 are 1, 7, 151, and 1057.
- Prime factors: The factors which are prime numbers. For example, 7 and 151 are prime factors of 1057.
- 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 1057 are (1, 1057) and (7, 151).
- Prime factorization: The expression of the number as the product of its prime factors. For example, 1057 is expressed as 7 × 151.
- Divisibility: The quality of a number being divisible by another number without leaving a remainder. For example, 1057 is divisible by 7.
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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.
