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 5005, how they are used in real life, and tips to learn them quickly.
The numbers that divide 5005 evenly are known as factors of 5005.
A factor of 5005 is a number that divides the number without remainder.
The factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 5005.
Negative factors of 5005: -1, -5, -7, -11, -13, -35, -55, -65, -77, -91, -143, -385, -5005.
Prime factors of 5005: 5, 7, 11, and 13.
Prime factorization of 5005: 5 × 7 × 11 × 13.
The sum of factors of 5005: 1 + 5 + 7 + 11 + 13 + 35 + 55 + 65 + 77 + 91 + 143 + 385 + 5005 = 5989
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 5005. Identifying the numbers which are multiplied to get the number 5005 is the multiplication method.
Step 1: Multiply 5005 by 1, 5005 × 1 = 5005.
Step 2: Check for other numbers that give 5005 after multiplying
5 × 1001 = 5005
7 × 715 = 5005
11 × 455 = 5005
13 × 385 = 5005
35 × 143 = 5005
55 × 91 = 5005
65 × 77 = 5005
Therefore, the positive factor pairs of 5005 are: (1, 5005), (5, 1001), (7, 715), (11, 455), (13, 385), (35, 143), (55, 91), (65, 77).
For every positive factor, there is a negative factor.
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 the simple division method
Step 1: Divide 5005 by 1, 5005 ÷ 1 = 5005.
Step 2: Continue dividing 5005 by the numbers until the remainder becomes 0.
5005 ÷ 1 = 5005
5005 ÷ 5 = 1001
5005 ÷ 7 = 715
5005 ÷ 11 = 455
5005 ÷ 13 = 385
5005 ÷ 35 = 143
5005 ÷ 55 = 91
5005 ÷ 65 = 77
Therefore, the factors of 5005 are: 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 5005.
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 5005 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5005 ÷ 5 = 1001
1001 ÷ 7 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1
The prime factors of 5005 are 5, 7, 11, and 13.
The prime factorization of 5005 is: 5 × 7 × 11 × 13.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 5005 is divided by 5 to get 1001.
Step 2: Now divide 1001 by 7 to get 143. Step 3: Then divide 143 by 11 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5005 is: 5 × 7 × 11 × 13.
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 5005: (1, 5005), (5, 1001), (7, 715), (11, 455), (13, 385), (35, 143), (55, 91), (65, 77).
Negative factor pairs of 5005: (-1, -5005), (-5, -1001), (-7, -715), (-11, -455), (-13, -385), (-35, -143), (-55, -91), (-65, -77).
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 teacher has 5005 pencils and wants to distribute them equally among 5 classes. How many pencils will each class receive?
Each class will receive 1001 pencils.
To distribute the pencils equally, we need to divide the total pencils by the number of classes.
5005 ÷ 5 = 1001
A garden is rectangular, the length of the garden is 77 meters, and the total area is 5005 square meters. Find the width.
The width is 65 meters.
To find the width of the garden, we use the formula,
Area = length × width
5005 = 77 × width
To find the value of width, we need to shift 77 to the left side.
5005 ÷ 77 = width
Width = 65
There are 143 students and 5005 candies. How many candies will each student get if divided equally?
Each student will get 35 candies.
To find the candies each student gets, divide the total candies by the students.
5005 ÷ 143 = 35
A company has 5005 units of product and needs to pack them into 385 boxes. How many units will each box contain?
Each box will contain 13 units.
Dividing the units by the total boxes gives the number of units per box.
5005 ÷ 385 = 13
5005 seats need to be arranged in 11 sections in a theater. How many seats will go in each section?
Each section will have 455 seats.
Divide the total seats by the sections.
5005 ÷ 11 = 455
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.