140 LearnersLast updated on May 30th, 2025
Factors of 1600
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 1600, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1600?
The numbers that divide 1600 evenly are known as factors of 1600.
A factor of 1600 is a number that divides the number without remainder.
The factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 400, 800, and 1600.
Negative factors of 1600: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -160, -200, -400, -800, and -1600.
Prime factors of 1600: 2 and 5.
Prime factorization of 1600: 26 × 52.
The sum of factors of 1600: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 160 + 200 + 400 + 800 + 1600 = 4655
How to Find Factors of 1600?
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 1600. Identifying the numbers which are multiplied to get the number 1600 is the multiplication method.
Step 1: Multiply 1600 by 1, 1600 ×1 = 1600.
Step 2: Check for other numbers that give 1600 after multiplying
2 × 800 = 1600
4 × 400 = 1600
5 × 320 = 1600
8 × 200 = 1600
10 ×160 = 1600
16 × 100 = 1600
20 × 80 = 1600
25 × 64 = 1600
32 × 50 = 1600
Therefore, the positive factor pairs of 1600 are: (1, 1600), (2, 800), (4, 400), (5, 320), (8, 200), (10, 160), (16, 100), (20, 80), (25, 64), (32, 50).
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 1600 by 1, 1600 ÷ 1 = 1600.
Step 2: Continue dividing 1600 by the numbers until the remainder becomes 0.
1600 ÷ 1 = 1600
1600 ÷ 2 = 800
1600 ÷ 4 = 400
1600 ÷ 5 = 320
1600 ÷ 8 = 200
1600 ÷10 = 160
1600 ÷ 16 = 100
1600 ÷ 20 = 80
1600 ÷ 25 = 64
1600 ÷ 32 = 50
Therefore, the factors of 1600 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 400, 800, 1600.
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:
- Prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1600 ÷ 2 = 80
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 1600 are 2 and 5.
The prime factorization of 1600 is: 22 × 52
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1600 is divided by 2 to get 800.
Step 2: Now divide 800 by 2 to get 400.
Step 3: Then divide 400 by 2 to get 200.
Step 4: Divide 200 by 2 to get 100.
Step 5: Divide 100 by 2 to get 50.
Step 6: Divide 50 by 2 to get 25.
Step 7: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1600 is: 26 × 52.
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 1600: (1, 1600), (2, 800), (4, 400), (5, 320), (8, 200), (10, 160), (16, 100), (20, 80), (25, 64), and (32, 50).
Negative factor pairs of 1600: (-1, -1600), (-2, -800), (-4, -400), (-5, -320), (-8, -200), (-10, -160), (-16, -100), (-20, -80), (-25, -64), and (-32, -50).
Common Mistakes and How to Avoid Them in Factors of 1600
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 1600, 1 and 1600 are also factors.
Mistake 2
Missing Negative Factors
We have used only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1600 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 1600/1.5 = 1066.67, 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 1600 are prime numbers.
For example, 2 and 5 are the prime factors of 1600, 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 1600 as 26 × 52 and missing all the key factors.
Factors of 1600 Examples
Problem 1
There are 16 teams and 1600 medals. How will they divide it equally?
They will get 100 medals each.
Explanation
To divide the medals equally, we need to divide the total medals by the number of teams. 1600/16 = 100
Problem 2
A plot is rectangular, the length of the plot is 50 meters and the total area is 1600 square meters. Find the width?
32 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1600 = 50 × width
To find the value of width, we need to shift 50 to the left side.
1600/50 = width
Width = 32.
Problem 3
There are 40 boxes and 1600 apples. How many apples will be in each box?
Each box will have 40 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes. 1600/40 = 40
Problem 4
In a class, there are 1600 students, and 80 groups. How many students are there in each group?
There are 20 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1600/80 = 20
Problem 5
1600 books need to be arranged in 32 shelves. How many books will go on each shelf?
Each of the shelves has 50 books.
Explanation
Divide total books by shelves.
1600/32 = 50
FAQs on Factors of 1600
1.What are the factors of 1600?
2.Mention the prime factors of 1600.
3.Is 1600, a multiple of 8?
4.Mention the factor pairs of 1600?
5.What is the square root of 1600?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 1600?
7.What are some fun ways kids in Vietnam can practice Factors of 1600 with numbers?
8.What role do numbers and Factors of 1600 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 1600 skills?
Important Glossaries for Factor of 1600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 400, 800, and 1600.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 1600.
- 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 1600 are (1, 1600), (2, 800), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1600 is 26 × 52.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 1600 is a multiple of 8.
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About BrightChamps in Vietnam
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.
