131 LearnersLast updated on May 26th, 2025
Factors of 1408
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 1408, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1408?
The numbers that divide 1408 evenly are known as factors of 1408.
A factor of 1408 is a number that divides the number without remainder.
The factors of 1408 are 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, and 1408.
Negative factors of 1408: -1, -2, -4, -8, -16, -32, -44, -88, -176, -352, -704, and -1408.
Prime factors of 1408: 2 and 11.
Prime factorization of 1408: 26 × 11.
The sum of factors of 1408: 1 + 2 + 4 + 8 + 16 + 32 + 44 + 88 + 176 + 352 + 704 + 1408 = 2835
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How to Find Factors of 1408?
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 1408. Identifying the numbers which are multiplied to get the number 1408 is the multiplication method.
Step 1: Multiply 1408 by 1, 1408 × 1 = 1408.
Step 2: Check for other numbers that give 1408 after multiplying
2 × 704 = 1408
4 × 352 = 1408
8 × 176 = 1408
16 × 88 = 1408
32 × 44 = 1408
Therefore, the positive factor pairs of 1408 are: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), (32, 44).
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 a simple division method
Step 1: Divide 1408 by 1, 1408 ÷ 1 = 1408.
Step 2: Continue dividing 1408 by the numbers until the remainder becomes 0.
1408 ÷ 1 = 1408
1408 ÷ 2 = 704
1408 ÷ 4 = 352
1408 ÷ 8 = 176
1408 ÷ 16 = 88
1408 ÷ 32 = 44
Therefore, the factors of 1408 are: 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, 1408.
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 1408 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1408 ÷ 2 = 704
704 ÷ 2 = 352
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
The prime factors of 1408 are 2 and 11. The prime factorization of 1408 is: 26 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1408 is divided by 2 to get 704.
Step 2: Now divide 704 by 2 to get 352.
Step 3: Then divide 352 by 2 to get 176.
Step 4: Continue dividing by 2 until you get 11.
Step 5: Finally divide 11 by 11 to get 1. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1408 is: 26 × 11.
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 1408: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), and (32, 44).
Negative factor pairs of 1408: (-1, -1408), (-2, -704), (-4, -352), (-8, -176), (-16, -88), and (-32, -44).
Common Mistakes and How to Avoid Them in Factors of 1408
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1408, 1 and 1408 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1408 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor of 1408 is incorrect because 1408/1.5 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 1408 are prime numbers is incorrect.
For instance, 2 and 11 are the prime factors of 1408, but it has other factors like 44 and 352.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1408 into 26 × 11 and missing all the key factors.
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Factors of 1408 Examples
Problem 1
There are 16 friends and 1408 candies. How will they divide it equally?
They will get 88 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1408/16 = 88
Problem 2
A field is rectangular, and the length of the field is 88 meters. The total area is 1408 square meters. Find the width.
16 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1408 = 88 × width
To find the value of width, we need to shift 88 to the left side.
1408/88 = width
Width = 16.
Problem 3
There are 32 bags and 1408 apples. How many apples will be in each bag?
Each bag will have 44 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
1408/32 = 44
Problem 4
In a school, there are 1408 students, and 44 classes. How many students are there in each class?
There are 32 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
1408/44 = 32
Problem 5
1408 books need to be arranged in 88 shelves. How many books will go on each shelf?
Each of the shelves has 16 books.
Explanation
Divide total books by shelves.
1408/88 = 16
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FAQs on Factors of 1408
1.What are the factors of 1408?
2.Mention the prime factors of 1408.
3.Is 1408 a multiple of 4?
4.Mention the factor pairs of 1408?
5.What is the square of 1408?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1408?
7.What are some fun ways kids in Bahrain can practice Factors of 1408 with numbers?
8.What role do numbers and Factors of 1408 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1408 skills?
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Important Glossaries for Factor of 1408
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1408 are 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, and 1408.
- Prime factors: The factors which are prime numbers. For example, 2 and 11 are prime factors of 1408.
- 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 1408 are (1, 1408), (2, 704), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1408 is 26 × 11.
- Multiple: The result of multiplying a number by an integer. For example, 1408 is a multiple of 4.
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About BrightChamps in Bahrain
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.
