130 LearnersLast updated on May 26th, 2025
Factors of 605
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 605, how they are used in real life, and tips to learn them quickly.
What are the Factors of 605?
The numbers that divide 605 evenly are known as factors of 605.
A factor of 605 is a number that divides the number without remainder.
The factors of 605 are 1, 5, 11, 55, 121, and 605.
Negative factors of 605: -1, -5, -11, -55, -121, and -605.
Prime factors of 605: 5 and 11.
Prime factorization of 605: 5 × 112.
The sum of factors of 605: 1 + 5 + 11 + 55 + 121 + 605 = 798
How to Find Factors of 605?
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 605. Identifying the numbers which are multiplied to get the number 605 is the multiplication method.
Step 1: Multiply 605 by 1, 605 × 1 = 605.
Step 2: Check for other numbers that give 605 after multiplying
5 × 121 = 605
11 × 55 = 605
Therefore, the positive factor pairs of 605 are: (1, 605), (5, 121), (11, 55). All these factor pairs result in 605. 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 605 by 1, 605 ÷ 1 = 605.
Step 2: Continue dividing 605 by the numbers until the remainder becomes 0.
605 ÷ 1 = 605
605 ÷ 5 = 121
605 ÷ 11 = 55
Therefore, the factors of 605 are: 1, 5, 11, 55, 121, 605.
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 605 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
605 ÷ 5 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factors of 605 are 5 and 11.
The prime factorization of 605 is: 5 × 11^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 605 is divided by 5 to get 121.
Step 2: Now divide 121 by 11 to get 11.
Step 3: Divide 11 by 11 to get 1. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 605 is: 5 × 112.
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 605: (1, 605), (5, 121), (11, 55).
Negative factor pairs of 605: (-1, -605), (-5, -121), (-11, -55).
Common Mistakes and How to Avoid Them in Factors of 605
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 605, 1 and 605 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 605 consist of -1, -5, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 605/2.5 = 242, 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 605 are prime numbers.
For example, 5 and 11 are the prime factors of 605, but it has other factors like 55, 121.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 605 as 5 × 11^2 and missing all the key factors.
Factors of 605 Examples
Problem 1
There are 5 teams and 605 points. How will they divide it equally?
They will get 121 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
605/5 = 121
Problem 2
A rectangular garden has a length of 11 meters and a total area of 605 square meters. Find the width.
55 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
605 = 11 × width
To find the value of width, we need to shift 11 to the left side.
605/11 = width
Width = 55.
Problem 3
There are 11 baskets and 605 apples. How many apples will be in each basket?
Each basket will have 55 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
605/11 = 55
Problem 4
In a school, there are 55 students, and they have a total of 605 books. How many books does each student get?
Each student gets 11 books.
Explanation
Dividing the books by the number of students, we will get the number of books each student receives.
605/55 = 11
Problem 5
605 pages need to be copied into 11 folders. How many pages will go into each folder?
Each folder will have 55 pages.
Explanation
Divide the total pages by the number of folders.
605/11 = 55
FAQs on Factors of 605
1.What are the factors of 605?
2.Mention the prime factors of 605.
3.Is 605 a multiple of 11?
4.Mention the factor pairs of 605?
5.What is the square of 605?
Important Glossaries for Factor of 605
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 605 are 1, 5, 11, 55, 121, and 605.
- Prime factors: The factors which are prime numbers. For example, 5 and 11 are prime factors of 605.
- 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 605 are (1, 605), (5, 121), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, 605 = 5 × 112.
- Multiples: The product of a number with an integer. For example, 605 is a multiple of 5 and 11.
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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.
