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 1020, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1020 evenly are known as factors of 1020.
A factor of 1020 is a number that divides the number without a remainder.
The factors of 1020 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, and 1020.
Negative factors of 1020: -1, -2, -3, -4, -5, -6, -10, -12, -15, -17, -20, -30, -34, -51, -60, -68, -85, -102, -170, -204, -255, -340, -510, and -1020.
Prime factors of 1020: 2, 3, 5, and 17.
Prime factorization of 1020: 22 × 3 × 5 × 17.
The sum of factors of 1020: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 17 + 20 + 30 + 34 + 51 + 60 + 68 + 85 + 102 + 170 + 204 + 255 + 340 + 510 + 1020 = 3060
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 1020. Identifying the numbers which are multiplied to get the number 1020 is the multiplication method.
Step 1: Multiply 1020 by 1, 1020 × 1 = 1020.
Step 2: Check for other numbers that give 1020 after multiplying:
2 × 510 = 1020
3 × 340 = 1020
4 × 255 = 1020
5 × 204 = 1020
6 × 170 = 1020
10 × 102 = 1020
12 × 85 = 1020
15 × 68 = 1020
17 × 60 = 1020
20 × 51 = 1020
30 × 34 = 1020
Therefore, the positive factor pairs of 1020 are: (1, 1020), (2, 510), (3, 340), (4, 255), (5, 204), (6, 170), (10, 102), (12, 85), (15, 68), (17, 60), (20, 51), (30, 34). 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 1020 by 1, 1020 ÷ 1 = 1020.
Step 2: Continue dividing 1020 by the numbers until the remainder becomes 0.
1020 ÷ 1 = 1020
1020 ÷ 2 = 510
1020 ÷ 3 = 340
1020 ÷ 4 = 255
1020 ÷ 5 = 204
1020 ÷ 6 = 170
1020 ÷ 10 = 102
1020 ÷ 12 = 85
1020 ÷ 15 = 68
1020 ÷ 17 = 60
1020 ÷ 20 = 51
1020 ÷ 30 = 34
Therefore, the factors of 1020 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, and 1020.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1020 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1020 ÷ 2 = 510
510 ÷ 2 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 1020 are 2, 3, 5, and 17.
The prime factorization of 1020 is: 2^2 × 3 × 5 × 17.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1020 is divided by 2 to get 510.
Step 2: Divide 510 by 2 to get 255.
Step 3: Then divide 255 by 3 to get 85.
Step 4: Divide 85 by 5 to get 17. Here, 17 is a prime number and cannot be divided further. So, the prime factorization of 1020 is: 22 × 3 × 5 × 17.
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 1020: (1, 1020), (2, 510), (3, 340), (4, 255), (5, 204), (6, 170), (10, 102), (12, 85), (15, 68), (17, 60), (20, 51), and (30, 34).
Negative factor pairs of 1020: (-1, -1020), (-2, -510), (-3, -340), (-4, -255), (-5, -204), (-6, -170), (-10, -102), (-12, -85), (-15, -68), (-17, -60), (-20, -51), and (-30, -34).
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 12 teams and 1020 apples. How will they divide them equally?
They will get 85 apples each.
To divide the apples equally, we need to divide the total apples by the number of teams.
1020/12 = 85
A rectangular garden has a length of 17 meters and a total area of 1020 square meters. Find the width.
60 meters.
To find the width of the garden, we use the formula,
Area = length × width
1020 = 17 × width
To find the value of width, we need to shift 17 to the left side.
1020/17 = width
Width = 60.
There are 30 boxes and 1020 candies. How many candies will be in each box?
Each box will have 34 candies.
To find the candies in each box, divide the total candies by the boxes.
1020/30 = 34
In a classroom, there are 1020 students and 5 sections. How many students are there in each section?
There are 204 students in each section.
Dividing the students by the total sections, we get the number of students in each section.
1020/5 = 204
1020 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 170 books.
Divide total books by shelves.
1020/6 = 170
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.