129 LearnersLast updated on May 26th, 2025
Factors of 1680
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.
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
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
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.
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.
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.
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).
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
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 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.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1680 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1680/1.5 = 1120, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1680 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of 1680, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1680 as 24 × 3 × 5 × 7 and missing all the key factors.
Factors of 1680 Examples
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?
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
Problem 2
A rectangular garden has a length of 30 meters and an area of 1680 square meters. Find the width of the garden.
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.
Problem 3
There are 280 boxes of chocolates and 1680 chocolates in total. How many chocolates are in each box?
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
Problem 4
A theater has 1680 seats and is divided into 21 sections. How many seats are in each section?
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
Problem 5
1680 tickets are to be equally distributed among 70 volunteers for an event. How many tickets will each volunteer get?
Each volunteer will get 24 tickets.
Explanation
Divide the total tickets by the number of volunteers.
1680/70 = 24
FAQs on Factors of 1680
1.What are the factors of 1680?
2.Mention the prime factors of 1680.
3.Is 1680 a multiple of 15?
4.Mention the factor pairs of 1680.
5.What is the square of 1680?
6.How can children in Philippines use numbers in everyday life to understand Factors of 1680?
7.What are some fun ways kids in Philippines can practice Factors of 1680 with numbers?
8.What role do numbers and Factors of 1680 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 1680 skills?
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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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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