124 LearnersLast updated on May 26th, 2025
Factors of 1051
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 1051, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1051?
The numbers that divide 1051 evenly are known as factors of 1051.
A factor of 1051 is a number that divides the number without remainder.
The factors of 1051 are 1, 23, 47, and 1051.
Negative factors of 1051: -1, -23, -47, and -1051.
Prime factors of 1051: 23 and 47.
Prime factorization of 1051: 23 × 47.
The sum of factors of 1051: 1 + 23 + 47 + 1051 = 1122
How to Find Factors of 1051?
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 1051. Identifying the numbers which are multiplied to get the number 1051 is the multiplication method.
Step 1: Multiply 1051 by 1, 1051 × 1 = 1051.
Step 2: Check for other numbers that give 1051 after multiplying 23 × 47 = 1051
Therefore, the positive factor pairs of 1051 are: (1, 1051) and (23, 47). All these factor pairs result in 1051. 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 a simple division method -
Step 1: Divide 1051 by 1, 1051 ÷ 1 = 1051.
Step 2: Continue dividing 1051 by the numbers until the remainder becomes 0.
1051 ÷ 1 = 1051
1051 ÷ 23 = 47
Therefore, the factors of 1051 are: 1, 23, 47, 1051.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1051 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1051 ÷ 23 = 47
47 ÷ 47 = 1
The prime factors of 1051 are 23 and 47.
The prime factorization of 1051 is: 23 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1051 is divided by 23 to get 47.
Step 2: Now divide 47 by 47 to get 1. Here, 47 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1051 is: 23 × 47.
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 1051: (1, 1051) and (23, 47).
Negative factor pairs of 1051: (-1, -1051) and (-23, -47).
Common Mistakes and How to Avoid Them in Factors of 1051
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 1051, 1 and 1051 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1051 consist of -1, -23, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1051/1.5 = 700.666..., which 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 1051 are prime numbers.
For example, 23 and 47 are the prime factors of 1051, but it also has other factors like 1 and 1051.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1051 as 23 × 47 and missing all the key factors.
Factors of 1051 Examples
Problem 1
There are 23 friends and 1051 marbles. How will they divide the marbles equally?
They will get 47 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
1051/23 = 47
Problem 2
A field is rectangular, the length of the field is 47 meters and the total area is 1051 square meters. Find the width?
23 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1051 = 47 × width
To find the value of width, we need to shift 47 to the left side.
1051/47 = width
Width = 23.
Problem 3
There are 47 boxes and 1051 chocolates. How many chocolates will be in each box?
Each box will have 23 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the number of boxes.
1051/47 = 23
Problem 4
In a class, there are 1051 students, and they are divided into 23 groups. How many students are there in each group?
There are 47 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1051/23 = 47
Problem 5
1051 books need to be arranged in 47 shelves. How many books will go on each shelf?
Each of the shelves has 23 books.
Explanation
Divide total books by shelves.
1051/47 = 23
FAQs on Factors of 1051
1.What are the factors of 1051?
2.Mention the prime factors of 1051.
3.Is 1051 a multiple of 23?
4.Mention the factor pairs of 1051?
5.What is the square of 1051?
Important Glossaries for Factors of 1051
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1051 are 1, 23, 47, and 1051.
- Prime factors: The factors which are prime numbers. For example, 23 and 47 are prime factors of 1051.
- 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 1051 are (1, 1051) and (23, 47).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1051 is 23 × 47.
- Multiple: A number that can be divided by another number without a remainder. For example, 1051 is a multiple of 23.
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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.
