200 LearnersLast updated on May 26th, 2025
Factors of 3200
Factors of 3200 are numbers that can divide 3200 completely without leaving a remainder. We often use factors in various practical situations, like organizing events and seating arrangements in our daily lives. In this topic, we will explore the factors of 3200 and the different methods to find them.
What are the Factors of 3200
The factors of 3200 are the numbers that divide 3200 evenly.
The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, and 3200.
Positive Factors: These are the positive numbers that divide 3200 evenly.
Positive factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, 3200
Negative Factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -125, -160, -200, -250, -400, -800, -1600, -3200
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 3200 as the product.
Prime factors of 3200: 2, 5
Prime Factorization: Prime factorization involves breaking down 3200 into its prime factors.
It is expressed as:
3200 = 27 × 52
Table listing the factors of 3200
|
Positive Factors |
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, 3200 |
|
Negative Factors |
-1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -125, -160, -200, -250, -400, -800, -1600, -3200 |
|
Prime Factors |
2, 5 |
|
Prime Factorization |
27 × 52 |
This breakdown helps in understanding the various factors of 3200, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 3200?
There are different methods to find the factors of 3200.
Methods to find the factors of 3200:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 3200 as their product.
Step 1: Find the pair of numbers whose product is 3200.
Step 2: The factors are those numbers, when multiplied, give 3200.
Step 3: Make a list of numbers whose product will be 3200.
A list of numbers whose products are 3200 is given below:
- 1 × 3200 = 3200
- 2 × 1600 = 3200
- 4 × 800 = 3200
- 5 × 640 = 3200
- 8 × 400 = 3200
- 10 × 320 = 3200
- 16 × 200 = 3200
- 20 × 160 = 3200
- 25 × 128 = 3200
- 32 × 100 = 3200
- 40 × 80 = 3200
- 50 × 64 = 3200
Thus, the factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, and 3200.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 3200÷1=3200
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, 3200.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.
Prime Factors of 3200: Number 3200 has only two prime factors.
Prime factors of 3200: 2, 5
To find the prime factors of 3200, we can divide 3200 with the prime numbers like 2 and 5 from the list of factors of 3200.
Step 1: Divide 3200 with the prime number 2
3200 ÷ 2 = 1600
Step 2: Divide 1600 with the prime number 2
1600 ÷ 2 = 800
Step 3: Divide 800 with the prime number 2
800 ÷ 2 = 400
Step 4: Divide 400 with the prime number 2
400 ÷ 2 = 200
Step 5: Divide 200 with the prime number 2
200 ÷ 2 = 100
Step 6: Divide 100 with the prime number 2
100 ÷ 2 = 50
Step 7: Divide 50 with the prime number 2
50 ÷ 2 = 25
Step 8: Divide 25 with the prime number 5
25 ÷ 5 = 5
Step 9: Divide 5 with the prime number 5
5 ÷ 5 = 1
Prime Factorization of 3200:
Prime Factorization breaks down the prime factors of 3200:
3200 = 27 × 52
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 3200 into its prime factors: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
In this factor tree, each branch splits into prime factors.
Positive and Negative Factor Pairs of 3200
Factors of 3200 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1,3200), (2,1600), (4,800), (5,640), (8,400), (10,320), (16,200), (20,160), (25,128), (32,100), (40,80), (50,64), (125,25), (160,20), (200,16), (250,12), (400,8), (800,4), (1600,2)
Negative Factor Pairs: (-1,-3200), (-2,-1600), (-4,-800), (-5,-640), (-8,-400), (-10,-320), (-16,-200), (-20,-160), (-25,-128), (-32,-100), (-40,-80), (-50,-64), (-125,-25), (-160,-20), (-200,-16), (-250,-12), (-400,-8), (-800,-4), (-1600,-2)
Common Mistakes and How to Avoid Them in Factors of 3200
Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming 5 as the only factor of 3200.
Since numbers ending in 0 or 5 are divisible by 5, you might think that 5 is the only factor of 3200. Remember that factors are numbers that can divide the given number equally. So, other numbers that can divide 3200 completely are 1, 2, 4, 8, 10, 16, 20, 25, 40, 50, 64, 80, 100, 125, 160, 200, 400, 800, 1600, and 3200.
Solved Examples for Factors of 3200
Problem 1
Can you check whether 75 and 3200 are co-prime?
No, 75 and 3200 are not co-prime.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 3200: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1600, 3200
Here, the GCF is 25. So 75 and 3200 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 3200 is a multiple of 7.
No, 3200 is not a multiple of 7.
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number.
No number can be multiplied by 7 to get 3200 as the product.
Problem 3
Identify the perfect square from the factors of 3200.
The perfect square factor of 3200 is 1600, and the root is 40.
Explanation
A perfect square is a number we get when the same number is multiplied twice.
When 40 is multiplied twice (40 × 40), we get the perfect square 1600.
Problem 4
Verify whether 25 is a factor of 3200.
Yes, 25 is a factor of 3200.
Explanation
A factor divides the number completely without leaving any remainder.
When 3200 is divided by 25, the result is 128, which is a whole number.
Problem 5
Find the smallest factor of 3200 greater than 10.
The smallest factor of 3200 greater than 10 is 16.
Explanation
The factors of 3200 greater than 10 are 16, 20, 25, etc.
The smallest among these is 16.
FAQs on Factors of 3200
1.What are the factors of 3200?
2.How do you determine if a number is a factor of 3200?
3.What is the smallest factor of 3200?
4.What is the largest factor of 3200?
5.How many factors does 3200 have?
6.How many odd factors does 3200 have?
7.What factors go into 3200?
8.Do any perfect squares exist in the factors of 3200?
Important glossaries for the Factors of 3200
- Factor: A number that divides another number completely without leaving a remainder.
- Prime Factor: A prime number that divides the given number exactly.
- Prime Factorization: The expression of a number as the product of its prime factors.
- Multiplication Method: A method used to find factors by multiplying pairs of numbers that result in the given number.
- Factor Tree: A diagram that visually represents the prime factorization of a number by breaking it down into its prime factors.
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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.
