116 LearnersLast updated on May 26th, 2025
Factors of 1059
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 1059, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1059?
The numbers that divide 1059 evenly are known as factors of 1059.
A factor of 1059 is a number that divides the number without remainder.
The factors of 1059 are 1, 3, 353, and 1059.
Negative factors of 1059: -1, -3, -353, and -1059.
Prime factors of 1059: 3 and 353.
Prime factorization of 1059: 3 × 353.
The sum of factors of 1059: 1 + 3 + 353 + 1059 = 1416
How to Find Factors of 1059?
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 1059. Identifying the numbers which are multiplied to get the number 1059 is the multiplication method.
Step 1: Multiply 1059 by 1, 1059 × 1 = 1059.
Step 2: Check for other numbers that give 1059 after multiplying 3 × 353 = 1059
Therefore, the positive factor pairs of 1059 are: (1, 1059) and (3, 353). All these factor pairs result in 1059. 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 1059 by 1, 1059 ÷ 1 = 1059.
Step 2: Continue dividing 1059 by the numbers until the remainder becomes 0.
1059 ÷ 1 = 1059
1059 ÷ 3 = 353
Therefore, the factors of 1059 are: 1, 3, 353, and 1059.
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 1059 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1059 ÷ 3 = 353 353 is a prime number and cannot be divided further.
The prime factors of 1059 are 3 and 353.
The prime factorization of 1059 is: 3 × 353.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1059 is divided by 3 to get 353
Step 2: 353 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1059 is: 3 × 353.
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 1059: (1, 1059) and (3, 353).
Negative factor pairs of 1059: (-1, -1059) and (-3, -353).
Common Mistakes and How to Avoid Them in Factors of 1059
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 1059, 1 and 1059 are also factors.
Mistake 2
Missing Negative Factors
We have used 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 1059 consist of -1, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor, because 1059/1.5 = 706, 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 1059 are prime numbers.
For example, 3 and 353 are the prime factors of 1059, but it has other factors like 1, 1059.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1059 as 3 × 353 and missing all the key factors.
Factors of 1059 Examples
Problem 1
There are 3 classrooms and 1059 chairs. How will they divide it equally?
They will get 353 chairs each.
Explanation
To divide the chairs equally, we need to divide the total chairs by the number of classrooms.
1059/3 = 353
Problem 2
A field is rectangular, the width of the field is 3 meters and the total area is 1059 square meters. Find the length?
353 meters.
Explanation
To find the length of the field, we use the formula,
Area = length × width
1059 = length × 3
To find the value of length, we need to shift 3 to the left side.
1059/3 = length
Length = 353.
Problem 3
There are 353 bags and 1059 books. How many books will be in each bag?
Each bag will have 3 books.
Explanation
To find the books in each bag, divide the total books by the bags.
1059/353 = 3
Problem 4
In a class, there are 1059 students, and 3 groups. How many students are there in each group?
There are 353 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1059/3 = 353
Problem 5
1059 pages need to be printed in 3 printers. How many pages will each printer handle?
Each of the printers will handle 353 pages.
Explanation
Divide total pages by printers.
1059/3 = 353
FAQs on Factors of 1059
1.What are the factors of 1059?
2.Mention the prime factors of 1059.
3.Is 1059 a multiple of 3?
4.Mention the factor pairs of 1059?
5.What is the square of 1059?
Important Glossaries for Factor of 1059
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1059 are 1, 3, 353, and 1059.
- Prime factors: The factors which are prime numbers. For example, 3 and 353 are prime factors of 1059.
- 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 1059 are (1, 1059) and (3, 353).
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1059 is 3 × 353.
- Multiples: The result of multiplying a number by an integer. For instance, 1059 is a multiple of 3.
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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.
