Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A gardener has 1764 flowers. How can they plant them in equal rows of 21 flowers each?
They can plant in 84 rows.
To divide the flowers equally, we need to divide the total flowers by the number of flowers in each row.
1764/21 = 84
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.
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.
There are 36 jars and 1764 candies. How many candies will be in each jar?
Each jar will have 49 candies.
To find the candies in each jar, divide the total candies by the jars.
1764/36 = 49
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.
Dividing the seats by the total sections, we will get the number of seats in each section.
1764/28 = 63
1764 books need to be arranged in 18 shelves. How many books will go on each shelf?
Each of the shelves has 98 books.
Divide total books by shelves.
1764/18 = 98
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.
: She loves to read number jokes and games.