157 LearnersLast updated on May 26th, 2025
Factors of 1764
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 1764, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1764?
The numbers that divide 1764 evenly are known as factors of 1764.
A factor of 1764 is a number that divides the number without remainder.
The factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, and 1764.
Negative factors of 1764: -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -49, -63, -84, -98, -126, -147, -196, -252, -294, -441, -588, -882, and -1764.
Prime factors of 1764: 2, 3, and 7.
Prime factorization of 1764: 2² × 3² × 7².
The sum of factors of 1764: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 49 + 63 + 84 + 98 + 126 + 147 + 196 + 252 + 294 + 441 + 588 + 882 + 1764 = 4968
How to Find Factors of 1764?
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 1764. Identifying the numbers which are multiplied to get the number 1764 is the multiplication method.
Step 1: Multiply 1764 by 1, 1764 × 1 = 1764.
Step 2: Check for other numbers that give 1764 after multiplying
2 × 882 = 1764
3 × 588 = 1764
4 × 441 = 1764
6 × 294 = 1764
7 × 252 = 1764
9 × 196 = 1764
12 × 147 = 1764
14 × 126 = 1764
18 × 98 = 1764
21 × 84 = 1764
28 × 63 = 1764
36 × 49 = 1764
Therefore, the positive factor pairs of 1764 are: (1, 1764), (2, 882), (3, 588), (4, 441), (6, 294), (7, 252), (9, 196), (12, 147), (14, 126), (18, 98), (21, 84), (28, 63), (36, 49).
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 1764 by 1, 1764 ÷ 1 = 1764.
Step 2: Continue dividing 1764 by the numbers until the remainder becomes 0.
1764 ÷ 1 = 1764
1764 ÷ 2 = 882
1764 ÷ 3 = 588
1764 ÷ 4 = 441
1764 ÷ 6 = 294
1764 ÷ 7 = 252
1764 ÷ 9 = 196
1764 ÷ 12 = 147
1764 ÷ 14 = 126
1764 ÷ 18 = 98
1764 ÷ 21 = 84
1764 ÷ 28 = 63
1764 ÷ 36 = 49
Therefore, the factors of 1764 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1764 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 1764 are 2, 3, and 7.
The prime factorization of 1764 is: 2² × 3² × 7².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1764 is divided by 2 to get 882.
Step 2: Now divide 882 by 2 to get 441.
Step 3: Then divide 441 by 3 to get 147.
Step 4: Divide 147 by 3 to get 49.
Step 5: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1764 is: 2² × 3² × 7².
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 1764: (1, 1764), (2, 882), (3, 588), (4, 441), (6, 294), (7, 252), (9, 196), (12, 147), (14, 126), (18, 98), (21, 84), (28, 63), (36, 49).
Negative factor pairs of 1764: (-1, -1764), (-2, -882), (-3, -588), (-4, -441), (-6, -294), (-7, -252), (-9, -196), (-12, -147), (-14, -126), (-18, -98), (-21, -84), (-28, -63), (-36, -49).
Common Mistakes and How to Avoid Them in Factors of 1764
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 1764, 1 and 1764 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1764 consist of -1, -2, -3, 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 1764/1.5 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 1764 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 1764, but it has other factors like 4, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 1764 as 2² × 3² × 7² and missing all the key factors.
Factors of 1764 Examples
Problem 1
A gardener has 1764 flowers. How can they plant them in equal rows of 21 flowers each?
They can plant in 84 rows.
Explanation
To divide the flowers equally, we need to divide the total flowers by the number of flowers in each row.
1764/21 = 84
Problem 2
An artist has a canvas that is 42 meters long with a total area of 1764 square meters. What is the width of the canvas?
42 meters.
Explanation
To find the width of the canvas, we use the formula,
Area = length × width
1764 = 42 × width
To find the value of width, we need to shift 42 to the left side.
1764/42 = width
Width = 42.
Problem 3
There are 36 jars and 1764 candies. How many candies will be in each jar?
Each jar will have 49 candies.
Explanation
To find the candies in each jar, divide the total candies by the jars.
1764/36 = 49
Problem 4
In a concert, there are 1764 seats, and 28 sections. How many seats are there in each section?
There are 63 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
1764/28 = 63
Problem 5
1764 books need to be arranged in 18 shelves. How many books will go on each shelf?
Each of the shelves has 98 books.
Explanation
Divide total books by shelves.
1764/18 = 98
FAQs on Factors of 1764
1.What are the factors of 1764?
2.Mention the prime factors of 1764.
3.Is 1764 a multiple of 7?
4.Mention the factor pairs of 1764?
5.What is the square of 1764?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1764?
7.What are some fun ways kids in Bahrain can practice Factors of 1764 with numbers?
8.What role do numbers and Factors of 1764 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1764 skills?
Important Glossaries for Factors of 1764
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1764 are 1, 2, 3, 4, 6, 7, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 1764.
- 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 1764 are (1, 1764), (2, 882), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, 1764 can be expressed as 2² × 3² × 7².
- Multiples: Numbers that can be obtained by multiplying a given number by an integer. For example, 1764 is a multiple of 7.
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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.
