Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 1820, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1820 evenly are known as factors of 1820.
A factor of 1820 is a number that divides the number without a remainder. The factors of 1820 are 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 35, 52, 65, 91, 130, 182, 260, 364, 455, 910, and 1820.
Negative factors of 1820: -1, -2, -4, -5, -7, -10, -13, -14, -20, -26, -35, -52, -65, -91, -130, -182, -260, -364, -455, -910, and -1820.
Prime factors of 1820: 2, 5, 7, 13.
Prime factorization of 1820: 2² × 5 × 7 × 13.
The sum of factors of 1820: 1 + 2 + 4 + 5 + 7 + 10 + 13 + 14 + 20 + 26 + 35 + 52 + 65 + 91 + 130 + 182 + 260 + 364 + 455 + 910 + 1820 = 4420
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify pairs of numbers that are multiplied to give 1820. Identifying the numbers which are multiplied to get the number 1820 is the multiplication method.
Step 1: Multiply 1820 by 1, 1820 × 1 = 1820.
Step 2: Check for other numbers that give 1820 after multiplying:
2 × 910 = 1820
4 × 455 = 1820
5 × 364 = 1820
7 × 260 = 1820
10 × 182 = 1820
13 × 140 = 1820
14 × 130 = 1820
20 × 91 = 1820
26 × 70 = 1820
35 × 52 = 1820
Therefore, the positive factor pairs of 1820 are: (1, 1820), (2, 910), (4, 455), (5, 364), (7, 260), (10, 182), (13, 140), (14, 130), (20, 91), (26, 70), and (35, 52).
For every positive factor, there is a negative factor.
Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 1820 by 1, 1820 ÷ 1 = 1820.
Step 2: Continue dividing 1820 by numbers until the remainder becomes 0.
1820 ÷ 1 = 1820
1820 ÷ 2 = 910
1820 ÷ 4 = 455
1820 ÷ 5 = 364
1820 ÷ 7 = 260
1820 ÷ 10 = 182
1820 ÷ 13 = 140
1820 ÷ 14 = 130
1820 ÷ 20 = 91
1820 ÷ 26 = 70
1820 ÷ 35 = 52
Therefore, the factors of 1820 are: 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 35, 52, 65, 91, 130, 182, 260, 364, 455, 910, and 1820.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1820 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1820 ÷ 2 = 910
910 ÷ 2 = 455
455 ÷ 5 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 1820 are 2, 5, 7, and 13.
The prime factorization of 1820 is: 2² × 5 × 7 × 13.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1820 is divided by 2 to get 910.
Step 2: Now divide 910 by 2 to get 455.
Step 3: Then divide 455 by 5 to get 91.
Step 4: Divide 91 by 7 to get 13.
Here, 13 is a prime number that cannot be divided anymore.
So, the prime factorization of 1820 is: 2² × 5 × 7 × 13.
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 1820: (1, 1820), (2, 910), (4, 455), (5, 364), (7, 260), (10, 182), (13, 140), (14, 130), (20, 91), (26, 70), and (35, 52).
Negative factor pairs of 1820: (-1, -1820), (-2, -910), (-4, -455), (-5, -364), (-7, -260), (-10, -182), (-13, -140), (-14, -130), (-20, -91), (-26, -70), and (-35, -52).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 14 people and 1820 sandwiches. How will they divide them equally?
They will get 130 sandwiches each.
To divide the sandwiches equally, we need to divide the total sandwiches by the number of people.
1820/14 = 130
A garden is rectangular, the length of the garden is 26 meters and the total area is 1820 square meters. Find the width?
70 meters.
To find the width of the garden, we use the formula,
Area = length × width
1820 = 26 × width
To find the value of width, we need to shift 26 to the left side.
1820/26 = width
Width = 70.
There are 35 baskets and 1820 apples. How many apples will be in each basket?
Each basket will have 52 apples.
To find the apples in each basket, divide the total apples by the baskets.
1820/35 = 52
In a conference, there are 1820 attendees, and 130 groups. How many attendees are there in each group?
There are 14 attendees in each group.
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1820/130 = 14
1820 books need to be arranged in 140 shelves. How many books will go on each shelf?
Each of the shelves has 13 books.
Divide total books by shelves.
1820/140 = 13
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.