Last updated on May 26th, 2025
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 561, how they are used in real life, and tips to learn them quickly.
The numbers that divide 561 evenly are known as factors of 561.
A factor of 561 is a number that divides the number without remainder.
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, and 561.
Negative factors of 561: -1, -3, -11, -17, -33, -51, -187, and -561.
Prime factors of 561: 3, 11, and 17.
Prime factorization of 561: 3 × 11 × 17.
The sum of factors of 561: 1 + 3 + 11 + 17 + 33 + 51 + 187 + 561 = 864
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 561. Identifying the numbers which are multiplied to get the number 561 is the multiplication method.
Step 1: Multiply 561 by 1, 561 × 1 = 561.
Step 2: Check for other numbers that give 561 after multiplying
3 × 187 = 561
11 × 51 = 561
17 × 33 = 561
Therefore, the positive factor pairs of 561 are: (1, 561), (3, 187), (11, 51), (17, 33). All these factor pairs result in 561. For every positive factor, there is a negative factor.
Dividing the given numbers with 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 561 by 1, 561 ÷ 1 = 561.
Step 2: Continue dividing 561 by the numbers until the remainder becomes 0.
561 ÷ 1 = 561
561 ÷ 3 = 187
561 ÷ 11 = 51
561 ÷ 17 = 33
Therefore, the factors of 561 are: 1, 3, 11, 17, 33, 51, 187, 561.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 561 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
561 ÷ 3 = 187
187 ÷ 11 = 17
17 ÷ 17 = 1
The prime factors of 561 are 3, 11, and 17.
The prime factorization of 561 is: 3 × 11 × 17.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 561 is divided by 3 to get 187.
Step 2: Now divide 187 by 11 to get 17.
Step 3: Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 561 is: 3 × 11 × 17.
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 561: (1, 561), (3, 187), (11, 51), and (17, 33).
Negative factor pairs of 561: (-1, -561), (-3, -187), (-11, -51), and (-17, -33).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A group of 3 people found 561 coins. How many coins will each person get if they divide them equally?
Each will get 187 coins.
To divide the coins equally, we need to divide the total coins by the number of people.
561/3 = 187
A theater has a seating arrangement where each row has 11 seats, and there are 561 seats in total. How many rows are there?
There are 51 rows.
To find the number of rows, we use the formula,
Total seats = number of rows × seats per row
561 = rows × 11
To find the value of rows, divide the total seats by seats per row.
561/11 = rows
Rows = 51
There are 17 baskets and 561 apples. How many apples will be in each basket if they are distributed equally?
Each basket will have 33 apples.
To find the apples in each basket, divide the total apples by the baskets.
561/17 = 33
A library has 561 books, and there are 11 shelves. How many books will go on each shelf?
Each of the shelves has 51 books.
Divide total books by shelves.
561/11 = 51
561 students are to be divided into 33 groups. How many students will be in each group?
There are 17 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
561/33 = 17
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.
: She loves to read number jokes and games.