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Last updated on May 26th, 2025

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Factors of 1680

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Factors are the numbers that divide a 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 1680, how they are used in real life, and tips to learn them quickly.

Factors of 1680 for Filipino Students
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What are the Factors of 1680?

The numbers that divide 1680 evenly are known as factors of 1680. A factor of 1680 is a number that divides the number without a remainder.

 

The factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.

 

Negative factors of 1680: -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -16, -20, -21, -24, -28, -30, -35, -40, -42, -48, -56, -60, -70, -84, -105, -120, -140, -168, -210, -240, -280, -336, -420, -560, -840, and -1680.

 

Prime factors of 1680: 2, 3, 5, and 7.

 

Prime factorization of 1680: 24 × 3 × 5 × 7.

 

The sum of the factors of 1680: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 48 + 56 + 60 + 70 + 84 + 105 + 120 + 140 + 168 + 210 + 240 + 280 + 336 + 420 + 560 + 840 + 1680 = 6552

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How to Find Factors of 1680?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1680. Identifying the numbers which are multiplied to get the number 1680 is the multiplication method.

 

Step 1: Multiply 1680 by 1, 1680 × 1 = 1680.

 

Step 2: Check for other numbers that give 1680 after multiplying

 

2 × 840 = 1680

3 × 560 = 1680

4 × 420 = 1680

5 × 336 = 1680

6 × 280 = 1680

7 × 240 = 1680

8 × 210 = 1680

10 × 168 = 1680

12 × 140 = 1680

14 × 120 = 1680

15 × 112 = 1680

16 × 105 = 1680

20 × 84 = 1680

21 × 80 = 1680

24 × 70 = 1680

28 × 60 = 1680

30 × 56 = 1680

35 × 48 = 1680

40 × 42 = 1680

 

Therefore, the positive factor pairs of 1680 are: (1, 1680), (2, 840), (3, 560), (4, 420), (5, 336), (6, 280), (7, 240), (8, 210), (10, 168), (12, 140), (14, 120), (15, 112), (16, 105), (20, 84), (21, 80), (24, 70), (28, 60), (30, 56), (35, 48), (40, 42).

 

For every positive factor, there is a negative factor.

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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 in whole numbers as factors. Factors can be calculated by following a simple division method

 

Step 1: Divide 1680 by 1, 1680 ÷ 1 = 1680.

 

Step 2: Continue dividing 1680 by the numbers until the remainder becomes 0.

 

1680 ÷ 1 = 1680

1680 ÷ 2 = 840

1680 ÷ 3 = 560

1680 ÷ 4 = 420

1680 ÷ 5 = 336

1680 ÷ 6 = 280

1680 ÷ 7 = 240

1680 ÷ 8 = 210

1680 ÷ 10 = 168

1680 ÷ 12 = 140

1680 ÷ 14 = 120

1680 ÷ 15 = 112

1680 ÷ 16 = 105

1680 ÷ 20 = 84

1680 ÷ 21 = 80

1680 ÷ 24 = 70

1680 ÷ 28 = 60

1680 ÷ 30 = 56

1680 ÷ 35 = 48

1680 ÷ 40 = 42

 

Therefore, the factors of 1680 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680.

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Prime Factors and Prime Factorization

The factors can be found by dividing them 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 1680 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

1680 ÷ 2 = 840

840 ÷ 2 = 420

420 ÷ 2 = 210

210 ÷ 2 = 105

105 ÷ 3 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

 

The prime factors of 1680 are 2, 3, 5, and 7.

 

The prime factorization of 1680 is: 24 × 3 × 5 × 7.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

 

Step 1: Firstly, 1680 is divided by 2 to get 840.

 

Step 2: Now divide 840 by 2 to get 420.

 

Step 3: Then divide 420 by 2 to get 210.

 

Step 4: Divide 210 by 2 to get 105.

 

Step 5: Divide 105 by 3 to get 35.

 

Step 6: Divide 35 by 5 to get 7. Here, 7 is a prime number that cannot be divided anymore. So, the prime factorization of 1680 is: 24 × 3 × 5 × 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 1680: (1, 1680), (2, 840), (3, 560), (4, 420), (5, 336), (6, 280), (7, 240), (8, 210), (10, 168), (12, 140), (14, 120), (15, 112), (16, 105), (20, 84), (21, 80), (24, 70), (28, 60), (30, 56), (35, 48), (40, 42).

 

Negative factor pairs of 1680: (-1, -1680), (-2, -840), (-3, -560), (-4, -420), (-5, -336), (-6, -280), (-7, -240), (-8, -210), (-10, -168), (-12, -140), (-14, -120), (-15, -112), (-16, -105), (-20, -84), (-21, -80), (-24, -70), (-28, -60), (-30, -56), (-35, -48), (-40, -42).

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Common Mistakes and How to Avoid Them in Factors of 1680

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

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Forgetting the number itself and 1 is a factor

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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 1680, 1 and 1680 are also factors.

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Factors of 1680 Examples

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Problem 1

A company has 1680 chairs and wants to arrange them in equal rows for a conference. If each row must have 40 chairs, how many rows will be there?

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There will be 42 rows.

Explanation

To find the number of rows, divide the total chairs by the number of chairs per row.

 

1680/40 = 42

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Problem 2

A rectangular garden has a length of 30 meters and an area of 1680 square meters. Find the width of the garden.

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56 meters.

Explanation

To find the width of the garden, we use the formula,

 

Area = length × width

 

1680 = 30 × width

 

To find the width, divide the area by the length.

 

1680/30 = width

 

Width = 56.

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Problem 3

There are 280 boxes of chocolates and 1680 chocolates in total. How many chocolates are in each box?

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Each box has 6 chocolates.

Explanation

To find the chocolates in each box, divide the total chocolates by the number of boxes.

 

1680/280 = 6

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Problem 4

A theater has 1680 seats and is divided into 21 sections. How many seats are in each section?

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There are 80 seats in each section.

Explanation

Dividing the total seats by the number of sections will give the number of seats in each section.

 

1680/21 = 80

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Problem 5

1680 tickets are to be equally distributed among 70 volunteers for an event. How many tickets will each volunteer get?

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Each volunteer will get 24 tickets.

Explanation

Divide the total tickets by the number of volunteers.

 

1680/70 = 24

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FAQs on Factors of 1680

1.What are the factors of 1680?

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2.Mention the prime factors of 1680.

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3.Is 1680 a multiple of 15?

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4.Mention the factor pairs of 1680.

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5.What is the square of 1680?

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6.How can children in Philippines use numbers in everyday life to understand Factors of 1680?

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7.What are some fun ways kids in Philippines can practice Factors of 1680 with numbers?

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8.What role do numbers and Factors of 1680 play in helping children in Philippines develop problem-solving skills?

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9.How can families in Philippines create number-rich environments to improve Factors of 1680 skills?

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Important Glossaries for Factors of 1680

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 1680.
     
  • 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 1680 are (1, 1680), (2, 840), etc.
     
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1680 is 24 × 3 × 5 × 7.
     
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, 2 × 840 = 1680.
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About BrightChamps in Philippines

At BrightChamps, numbers are more than just digits—they open doors to countless opportunities! Our goal is to help kids across the Philippines build essential math skills, with today’s focus on Factors of 1680 highlighting factors—in a fun, lively, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy gadgets, strong number skills give them confidence for everyday tasks. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different ways, we customize our approach to each child. From Manila’s busy streets to Palawan’s beautiful islands, BrightChamps brings math to life across the Philippines. Let’s make factors a fun part of every child’s math story!
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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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Fun Fact

: She loves to read number jokes and games.

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