267 LearnersLast updated on May 26th, 2025
Factors of 6400
Factors of 6400 are numbers that can divide 6400 completely without leaving a remainder. We often use factors in activities like organizing events or seating arrangements in our daily lives. In this topic, we will explore the factors of 6400 and the different methods to find them.
What are the Factors of 6400?
The factors of 6400 are the numbers that can divide 6400 completely without any remainder.
The factors of 6400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.
Positive Factors: The positive factors of 6400 are all the numbers that can divide 6400 evenly. These are:
Positive factors of 6400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, 6400.
Negative Factors: These are the negative counterparts of the positive factors.
Negative factors of 6400: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -256, -400, -512, -800, -1600, -6400.
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 6400 as the product.
Prime factors of 6400: 2, 5.
Prime Factorization: Prime factorization involves breaking 6400 into its prime factors. The prime factorization of 6400 is expressed as:
Prime Factorization of 6400: 27 × 52.
Table listing the factors of 6400
|
Positive Factors |
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, 6400 |
|
Negative Factors |
-1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -256, -400, -512, -800, -1600, -6400 |
|
Prime Factors |
2, 5 |
|
Prime Factorization |
27 × 52 |
This breakdown helps in understanding the various factors of 6400, whether they are positive or negative, as well as how prime factorization works for this number.
Table listing the factors of 6400
There are several methods to find the factors of 6400:
Methods to find the factors of 6400:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using the Multiplication Method
The multiplication method involves finding the pair of numbers whose product is 6400.
Step 1: Find the pair of numbers whose product is 6400.
Step 2: The factors are those numbers that, when multiplied, give 6400.
Step 3: Make a list of numbers whose product will be 6400.
A list of numbers whose products are 6400 is given below:
- 1 × 6400 = 6400
- 2 × 3200 = 6400
- 4 × 1600 = 6400
- 5 × 1280 = 6400
- 8 × 800 = 6400
- 10 × 640 = 6400
- 16 × 400 = 6400
- 20 × 320 = 6400
- 25 × 256 = 6400
- 32 × 200 = 6400
- 40 × 160 = 6400
- 50 × 128 = 6400
- 64 × 100 = 6400
- 80 × 80 = 6400
Thus, the factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.
Finding Factors Using the Division Method
The division method finds the numbers that completely divide the given number. The steps are as follows:
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Step 2: Move to the next integer. The factors of 6400 include the number that is used to divide and the quotient.
Thus, the factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number and expressed in the form of prime factors, is its prime factorization.
Prime Factors of 6400: 2, 5.
To find the prime factors of 6400, we can divide 6400 by prime numbers like 2 and 5 from the list of factors of 6400.
Step 1: Divide 6400 by the prime number 2:
- 6400 ÷ 2 = 3200
- 3200 ÷ 2 = 1600
- 1600 ÷ 2 = 800
- 800 ÷ 2 = 400
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
Step 2: Now divide 25 by the prime number 5:
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Prime Factorization of 6400: 6400 = 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 6400 into its prime factors: 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 6400
Factors of 6400 can be written in both positive and negative pairs. These are like team members, and their product will be equal to the number 6400.
Positive Factor Pairs:
(1, 6400), (2, 3200), (4, 1600), (5, 1280), (8, 800), (10, 640), (16, 400), (20, 320), (25, 256), (32, 200), (40, 160), (50, 128), (64, 100), (80, 80).
Negative Factor Pairs:
(-1, -6400), (-2, -3200), (-4, -1600), (-5, -1280), (-8, -800), (-10, -640), (-16, -400), (-20, -320), (-25, -256), (-32, -200), (-40, -160), (-50, -128), (-64, -100), (-80, -80).
Common Mistakes and How to Avoid Them in Factors of 6400
Mistakes are those steps that help us to understand more about something. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming a single factor like 5 is the only factor of 6400.
Remember that factors are numbers that can divide the given number completely. For 6400, the factors include many more numbers like 1, 2, 4, 8, 10, 16, and so on.
Solved Examples for Factors of 6400
Problem 1
Can you check whether 75 and 25 are co-prime with respect to the factors of 6400?
No, 75 and 25 are not co-prime with respect to the factors of 6400.
Explanation
To check whether 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 25: 1, 5, 25
Factors of 6400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 256, 400, 512, 640, 800, 1600, 3200, 6400
Here, the GCF of 75 and 25 is 25, which is greater than 1. So, 75 and 25 are not co-prime.
Problem 2
Verify whether 75 is a multiple of 7 considering the factors of 6400.
No, 75 is not a multiple of 7 with respect to the factors of 6400.
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number. No number can be multiplied by 7 to get 75 as the product, and 75 is not among the multiples of 7 in the factors of 6400.
Problem 3
Identify the perfect square from the factors of 6400.
The perfect square factors of 6400 are 1, 4, 25, 100, 400, 1600, and 6400.
Explanation
A perfect square is a number that results from multiplying the same number twice. For example, 25 is a perfect square because 5×5 = 25, and similarly, 100 is a perfect square because 10×10 = 100.
Problem 4
Is 6400 divisible by 200?
Yes, 6400 is divisible by 200.
Explanation
To check divisibility, divide 6400 by 200.
6400 ÷ 200 = 32
Since the result is a whole number, 6400 is divisible by 200.
Problem 5
Find the common factors of 75 and 6400.
The common factors of 75 and 6400 are 1, 5, 25.
Explanation
To find the common factors, list the factors of both numbers and identify the ones they share.
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 6400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 256, 400, 512, 640, 800, 1600, 3200, 6400
The common factors are 1, 5, and 25.
FAQs on Factors of 6400
1.What are the factors of 6400?
2.How do you determine if a number is a factor of 6400?
3.What is the smallest factor of 6400?
4.What is the largest factor of 6400?
5.How many factors does 6400 have?
6.How many odd factors does 6400 have?
7.What factors go into 6400?
8.Do any perfect squares exist in the factors of 6400?
Important glossaries for the Factors of 6400
- Factors: Numbers that can divide a given number completely without leaving a remainder.
- Prime Factors: Prime numbers that, when multiplied together, give the original number.
- Prime Factorization: Breaking down a number into its prime factors.
- Perfect Square: A number that is the product of a number multiplied by itself.
- Multiple: Numbers we get when a number is multiplied by any integer.
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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.
