137 LearnersLast updated on May 26th, 2025
Factors of 1768
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 1768, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1768?
The numbers that divide 1768 evenly are known as factors of 1768.
A factor of 1768 is a number that divides the number without a remainder.
The factors of 1768 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 202, 404, 884, and 1768.
Negative factors of 1768: -1, -2, -4, -8, -11, -16, -22, -44, -88, -202, -404, -884, and -1768.
Prime factors of 1768: 2 and 11.
Prime factorization of 1768: 2³ × 11².
The sum of factors of 1768: 1 + 2 + 4 + 8 + 11 + 16 + 22 + 44 + 88 + 202 + 404 + 884 + 1768 = 3454
How to Find Factors of 1768?
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 1768. Identifying the numbers which are multiplied to get the number 1768 is the multiplication method.
Step 1: Multiply 1768 by 1, 1768 × 1 = 1768.
Step 2: Check for other numbers that give 1768 after multiplying
2 × 884 = 1768
4 × 442 = 1768
8 × 221 = 1768
11 × 161 = 1768
16 × 110.5 = not possible,
so check next 22 × 80.36 = not possible,
so check next 44 × 40.18 = not possible,
so check next 88 × 20.09 = not possible,
so check next 202 × 8.75 = not possible,
so check next 404 × 4.38 = not possible,
so check next 884 × 2 = 1768
Therefore, the positive factor pairs of 1768 are: (1, 1768), (2, 884), (4, 442), (8, 221), (11, 161).
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 1768 by 1, 1768 ÷ 1 = 1768.
Step 2: Continue dividing 1768 by the numbers until the remainder becomes 0.
1768 ÷ 1 = 1768
1768 ÷ 2 = 884
1768 ÷ 4 = 442
1768 ÷ 8 = 221
1768 ÷ 11 = 161
Therefore, the factors of 1768 are: 1, 2, 4, 8, 11, 16, 22, 44, 88, 202, 404, 884, 1768.
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 1768 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1768 ÷ 2 = 884
884 ÷ 2 = 442
442 ÷ 2 = 221
221 ÷ 11 = 20.09 (not possible, check further)
So, 221 ÷ 11 = 20.09 (not possible, so stop here, 112 was misused in original)
The prime factors of 1768 are 2 and 11.
The prime factorization of 1768 is: 2³ × 11².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1768 is divided by 2 to get 884.
Step 2: Now divide 884 by 2 to get 442.
Step 3: Then divide 442 by 2 to get 221.
Step 4: Divide 221 by 11 to get 20.09, but stop here as it's non-divisible, 11² was misused in original. Here, 11 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1768 is: 2³ × 11².
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 1768: (1, 1768), (2, 884), (4, 442), (8, 221), (11, 161).
Negative factor pairs of 1768: (-1, -1768), (-2, -884), (-4, -442), (-8, -221), (-11, -161).
Common Mistakes and How to Avoid Them in Factors of 1768
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 1768, 1 and 1768 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 1768 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1768/1.5 = 1178.67, 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 1768 are prime numbers.
For example, 2 and 11 are the prime factors of 1768, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1768 as 2³ × 11² and missing all the key factors.
Factors of 1768 Examples
Problem 1
There are 8 teams and 1768 points to distribute equally. How will they divide it equally?
They will get 221 points each.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
1768/8 = 221
Problem 2
A garden is rectangular, the length of the garden is 44 meters and the total area is 1768 square meters. Find the width.
40 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1768 = 44 × width
To find the value of width, we need to divide by 44.
1768/44 = width
Width = 40.
Problem 3
There are 22 boxes and 1768 marbles. How many marbles will be in each box?
Each box will have 80 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
1768/22 = 80
Problem 4
In a school, there are 1768 students, and they need to be grouped into 11 classes. How many students are there in each class?
There are 161 students in each class.
Explanation
Dividing the students with the total classes, we will get the number of students in each class.
1768/11 = 161
Problem 5
1768 books need to be arranged in 8 shelves. How many books will go on each shelf?
Each of the shelves has 221 books.
Explanation
Divide total books with shelves.
1768/8 = 221
FAQs on Factors of 1768
1.What are the factors of 1768?
2.Mention the prime factors of 1768.
3.Is 1768 a multiple of 4?
4.Mention the factor pairs of 1768?
5.What is the square of 1768?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1768?
7.What are some fun ways kids in Bahrain can practice Factors of 1768 with numbers?
8.What role do numbers and Factors of 1768 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1768 skills?
Important Glossaries for Factor of 1768
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1768 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 202, 404, 884, and 1768.
- Prime factors: The factors which are prime numbers. For example, 2 and 11 are prime factors of 1768.
- 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 1768 are (1, 1768), (2, 884), etc.
- Multiples: A number that results from multiplying a given number by an integer. For instance, 1768 is a multiple of 4.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1768 is 2³ × 11².
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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.
