122 LearnersLast updated on May 26th, 2025
Factors of 3500
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 3500, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3500?
The numbers that divide 3500 evenly are known as factors of 3500.
A factor of 3500 is a number that divides the number without remainder.
The factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 250, 350, 500, 700, 875, 1750, and 3500.
Negative factors of 3500: -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -250, -350, -500, -700, -875, -1750, and -3500.
Prime factors of 3500: 2, 5, and 7.
Prime factorization of 3500: 22 × 52 × 7 × 10.
The sum of factors of 3500: 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 140 + 175 + 250 + 350 + 500 + 700 + 875 + 1750 + 3500 = 9306
How to Find Factors of 3500?
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 3500. Identifying the numbers which are multiplied to get the number 3500 is the multiplication method.
Step 1: Multiply 3500 by 1, 3500 × 1 = 3500.
Step 2: Check for other numbers that give 3500 after multiplying
2 × 1750 = 3500
4 × 875 = 3500
5 × 700 = 3500
7 × 500 = 3500
10 × 350 = 3500
14 × 250 = 3500
20 × 175 = 3500
25 × 140 = 3500
28 × 125 = 3500
35 × 100 = 3500
50 × 70 = 3500
Therefore, the positive factor pairs of 3500 are: (1, 3500), (2, 1750), (4, 875), (5, 700), (7, 500), (10, 350), (14, 250), (20, 175), (25, 140), (28, 125), (35, 100), (50, 70). 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 the simple division method -
Step 1: Divide 3500 by 1, 3500 ÷ 1 = 3500.
Step 2: Continue dividing 3500 by the numbers until the remainder becomes 0.
3500 ÷ 1 = 3500
3500 ÷ 2 = 1750
3500 ÷ 4 = 875
3500 ÷ 5 = 700
3500 ÷ 7 = 500
3500 ÷ 10 = 350
3500 ÷ 14 = 250
3500 ÷ 20 = 175
3500 ÷ 25 = 140
3500 ÷ 28 = 125
3500 ÷ 35 = 100
3500 ÷ 50 = 70
Therefore, the factors of 3500 are: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
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 3500 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3500 ÷ 2 = 1750
1750 ÷ 2 = 875
875 ÷ 5 = 175
175 ÷ 5 = 35
35 ÷ 7 = 5
5 ÷ 5 = 1
The prime factors of 3500 are 2, 5, and 7.
The prime factorization of 3500 is: 22 × 52 × 7 × 10.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3500 is divided by 2 to get 1750.
Step 2: Now divide 1750 by 2 to get 875.
Step 3: Then divide 875 by 5 to get 175.
Step 4: Divide 175 by 5 to get 35.
Step 5: Divide 35 by 7 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3500 is: 22 × 52 × 7 × 10.
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 3500: (1, 3500), (2, 1750), (4, 875), (5, 700), (7, 500), (10, 350), (14, 250), (20, 175), (25, 140), (28, 125), (35, 100), (50, 70).
Negative factor pairs of 3500: (-1, -3500), (-2, -1750), (-4, -875), (-5, -700), (-7, -500), (-10, -350), (-14, -250), (-20, -175), (-25, -140), (-28, -125), (-35, -100), (-50, -70).
Common Mistakes and How to Avoid Them in Factors of 3500
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 3500, 1 and 3500 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 3500 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 3500/1.5 = 2333.333, 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 3500 are prime numbers. For example, 2, 5, and 7 are the prime factors of 3500, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3500 as 2^2 × 5^2 × 7 and missing all the key factors.
Factors of 3500 Examples
Problem 1
There are 14 buses and 3500 passengers. How will they distribute them equally?
Each bus will have 250 passengers.
Explanation
To divide the passengers equally, we need to divide the total passengers by the number of buses.
3500/14 = 250
Problem 2
A garden is rectangular, the length of the garden is 70 meters and the total area is 3500 square meters. Find the width?
50 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
3500 = 70 × width
To find the value of width, we need to shift 70 to the left side.
3500/70 = width
Width = 50.
Problem 3
There are 25 boxes and 3500 apples. How many apples will be in each box?
Each box will have 140 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
3500/25 = 140
Problem 4
In a community, there are 3500 members, and 70 groups. How many members are there in each group?
There are 50 members in each group.
Explanation
Dividing the members by the total groups, we will get the number of members in each group.
3500/70 = 50
Problem 5
3500 books need to be arranged in 140 shelves. How many books will go on each shelf?
Each of the shelves has 25 books.
Explanation
Divide total books by shelves.
3500/140 = 25
FAQs on Factors of 3500
1.What are the factors of 3500?
2.Mention the prime factors of 3500.
3.Is 3500 a multiple of 25?
4.Mention the factor pairs of 3500?
5.What is the square of 3500?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 3500?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 3500 with numbers?
8.What role do numbers and Factors of 3500 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 3500 skills?
Important Glossaries for Factor of 3500
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 3500.
- 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 3500 are (1, 3500), (2, 1750), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 3500 is 22 × 52 × 7 × 10.
- Multiple: A number that can be divided by another number without a remainder. For instance, 3500 is a multiple of 25.
Explore More numbers
About BrightChamps in United Arab Emirates
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.
