117 LearnersLast updated on May 26th, 2025
Factors of 840
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 and arranging things. In this topic, we will learn about the factors of 840, how they are used in real life, and tips to learn them quickly.
What are the Factors of 840?
The numbers that divide 840 evenly are known as factors of 840.
A factor of 840 is a number that divides the number without a remainder.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
Negative factors of 840: -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -28, -30, -35, -40, -42, -56, -60, -70, -84, -105, -120, -140, -168, -210, -280, -420, and -840.
Prime factors of 840: 2, 3, 5, and 7.
Prime factorization of 840: (23 x 3 x 5 x 7).
The sum of factors of 840: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 56 + 60 + 70 + 84 + 105 + 120 + 140 + 168 + 210 + 280 + 420 + 840 = 2,232
How to Find Factors of 840?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 840. Identifying the numbers which are multiplied to get the number 840 is the multiplication method.
Step 1: Multiply 840 by 1, 840 × 1 = 840.
Step 2: Check for other numbers that give 840 after multiplying
(2 x 420 = 840)
(3 x 280 = 840)
(4 x 210 = 840)
(5 x 168 = 840)
(6 x 140 = 840)
(7 x 120 = 840)
(8 x 105 = 840)
(10 x 84 = 840)
(12 x 70 = 840)
(14 x 60 = 840)
(15 x 56 = 840)
(20 x 42 = 840)
(21 x 40 = 840)
(24 x 35 = 840)
(28 x 30 = 840)
Therefore, the positive factor pairs of 840 are: (1, 840), (2, 420), (3, 280), (4, 210), (5, 168), (6, 140), (7, 120), (8, 105), (10, 84), (12, 70), (14, 60), (15, 56), (20, 42), (21, 40), (24, 35), and (28, 30).
every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 840 by 1, 840 ÷ 1 = 840.
Step 2: Continue dividing 840 by the numbers until the remainder becomes 0.
840 ÷ 1 = 840
840 ÷ 2 = 420
840 ÷ 3 = 280
840 ÷ 4 = 210
840 ÷ 5 = 168
840 ÷ 6 = 140
840 ÷ 7 = 120
840 ÷ 8 = 105
840 ÷ 10 = 84
840 ÷ 12 = 70
840 ÷ 14 = 60
840 ÷ 15 = 56
840 ÷ 20 = 42
840 ÷ 21 = 40
840 ÷ 24 = 35
840 ÷ 28 = 30
Therefore, the factors of 840 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 840 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
840 ÷ 2 = 420
420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 840 are 2, 3, 5, and 7.
The prime factorization of 840 is: (23 x 3 x 5 x 7).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 840 is divided by 2 to get 420.
Step 2: Now divide 420 by 2 to get 210.
Step 3: Then divide 210 by 2 to get 105.
Step 4: Divide 105 by 3 to get 35.
Step 5: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 840 is: (23 x 3 x 5 x 7).
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 840: (1, 840), (2, 420), (3, 280), (4, 210), (5, 168), (6, 140), (7, 120), (8, 105), (10, 84), (12, 70), (14, 60), (15, 56), (20, 42), (21, 40), (24, 35), and (28, 30).
- Negative factor pairs of 840: (-1, -840), (-2, -420), (-3, -280), (-4, -210), (-5, -168), (-6, -140), (-7, -120), (-8, -105), (-10, -84), (-12, -70), (-14, -60), (-15, -56), (-20, -42), (-21, -40), (-24, -35), and (-28, -30).
Common Mistakes and How to Avoid Them in Factors of 840
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 factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 840, 1 and 840 are also factors.
Factors of 840 Examples
Problem 1
There are 14 teams and 840 tickets. How will they distribute it equally?
They will get 60 tickets each.
Explanation
To distribute the tickets equally, we need to divide the total tickets by the number of teams.
840/14 = 60
Problem 2
A garden is rectangular, the length of the garden is 21 meters, and the total area is 840 square meters. Find the width.
40 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
840 = 21 × width
To find the value of width, we need to shift 21 to the left side.
840/21 = width
Width = 40.
Problem 3
There are 35 boxes and 840 oranges. How many oranges will be in each box?
Each box will have 24 oranges.
Explanation
To find the oranges in each box, divide the total oranges by the boxes.
840/35 = 24
Problem 4
In a seminar, there are 840 participants, and 7 groups. How many participants are there in each group?
There are 120 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
840/7 = 120
Problem 5
840 plants need to be arranged in 12 rows. How many plants will go in each row?
Each row will have 70 plants.
Explanation
Divide total plants by rows.
840/12 = 70
FAQs on Factors of 840
1.What are the factors of 840?
2.Mention the prime factors of 840.
3.Is 840 a multiple of 7?
4.Mention the factor pairs of 840?
5.What is the square of 840?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 840?
7.What are some fun ways kids in Vietnam can practice Factors of 840 with numbers?
8.What role do numbers and Factors of 840 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 840 skills?
Important Glossaries for Factor of 840
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 840.
- 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 840 are (1, 840), (2, 420), and so on.
- Prime factorization: The method of expressing a number as the product of its prime factors. For example, the prime factorization of 840 is (23 x 3 x 5 x 7).
- Division method: A way to find factors by dividing the number by natural numbers to see which divisions result in a whole number.
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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.
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