119 LearnersLast updated on May 26th, 2025
Factors of 2940
Factors are the numbers that divide any given number evenly without 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 2940, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 2940?
The numbers that divide 2940 evenly are known as factors of 2940.
A factor of 2940 is a number that divides the number without remainder.
The factors of 2940 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 49, 60, 70, 84, 98, 105, 140, 147, 196, 210, 294, 420, 490, 588, 735, 980, 1470, and 2940.
Negative factors of 2940: -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -28, -30, -35, -42, -49, -60, -70, -84, -98, -105, -140, -147, -196, -210, -294, -420, -490, -588, -735, -980, -1470, and -2940.
Prime factors of 2940: 2, 3, 5, and 7.
Prime factorization of 2940: 22 × 3 × 5 × 72.
The sum of factors of 2940: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 28 + 30 + 35 + 42 + 49 + 60 + 70 + 84 + 98 + 105 + 140 + 147 + 196 + 210 + 294 + 420 + 490 + 588 + 735 + 980 + 1470 + 2940 = 9360
How to Find Factors of 2940?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 2940. Identifying the numbers which are multiplied to get the number 2940 is the multiplication method.
Step 1: Multiply 2940 by 1, 2940 × 1 = 2940.
Step 2: Check for other numbers that give 2940 after multiplying
2 × 1470 = 2940
3 × 980 = 2940
5 × 588 = 2940
6 × 490 = 2940
7 × 420 = 2940
10 × 294 = 2940
14 × 210 = 2940
15 × 196 = 2940
20 × 147 = 2940
21 × 140 = 2940
28 × 105 = 2940
30 × 98 = 2940
35 × 84 = 2940
42 × 70 = 2940
49 × 60 = 2940
Therefore, the positive factor pairs of 2940 are: (1, 2940), (2, 1470), (3, 980), (4, 735), (5, 588), (6, 490), (7, 420), (10, 294), (12, 245), (14, 210), (15, 196), (20, 147), (21, 140), (28, 105), (30, 98), (35, 84), (42, 70), and (49, 60). All these factor pairs result in 2940. 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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2940 by 1, 2940 ÷ 1 = 2940.
Step 2: Continue dividing 2940 by the numbers until the remainder becomes 0.
2940 ÷ 1 = 2940
2940 ÷ 2 = 1470
2940 ÷ 3 = 980
2940 ÷ 5 = 588
2940 ÷ 6 = 490
2940 ÷ 7 = 420
2940 ÷ 10 = 294
2940 ÷ 12 = 245
2940 ÷ 14 = 210
2940 ÷ 15 = 196
2940 ÷ 20 = 147
2940 ÷ 21 = 140
2940 ÷ 28 = 105
2940 ÷ 30 = 98
2940 ÷ 35 = 84
2940 ÷ 42 = 70
2940 ÷ 49 = 60
Therefore, the factors of 2940 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 49, 60, 70, 84, 98, 105, 140, 147, 196, 210, 294, 420, 490, 588, 735, 980, 1470, and 2940.
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 2940 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2940 ÷ 2 = 1470
1470 ÷ 2 = 735
735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 2940 are 2, 3, 5, and 7.
The prime factorization of 2940 is: 2^2 × 3 × 5 × 7^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2940 is divided by 2 to get 1470.
Step 2: Now divide 1470 by 2 to get 735.
Step 3: Then divide 735 by 3 to get 245.
Step 4: Divide 245 by 5 to get 49.
Step 5: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 2940 is: 22 × 3 × 5 × 72.
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 2940: (1, 2940), (2, 1470), (3, 980), (4, 735), (5, 588), (6, 490), (7, 420), (10, 294), (12, 245), (14, 210), (15, 196), (20, 147), (21, 140), (28, 105), (30, 98), (35, 84), (42, 70), and (49, 60).
Negative factor pairs of 2940: (-1, -2940), (-2, -1470), (-3, -980), (-4, -735), (-5, -588), (-6, -490), (-7, -420), (-10, -294), (-12, -245), (-14, -210), (-15, -196), (-20, -147), (-21, -140), (-28, -105), (-30, -98), (-35, -84), (-42, -70), and (-49, -60).
Common Mistakes and How to Avoid Them in Factors of 2940
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 word. Always remember to include 1 and the number itself.
For example, in factors of 2940, 1 and 2940 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 2940 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 2940/1.5 = 1960, 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 2940 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of 2940, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 2940 as 2^2 × 3 × 5 × 7^2 and missing all the key factors.
Factors of 2940 Examples
Problem 1
There are 2940 marbles and 14 bags. How many marbles will each bag contain?
Each bag will contain 210 marbles.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of bags.
2940/14 = 210
Problem 2
A rectangular pool has an area of 2940 square meters and a length of 42 meters. What is the width of the pool?
The width of the pool is 70 meters.
Explanation
To find the width of the pool, we use the formula,
Area = length × width
2940 = 42 × width
To find the value of width, we need to shift 42 to the left side.
2940/42 = width
Width = 70.
Problem 3
A farmer has 2940 apples and wants to distribute them equally among 35 baskets. How many apples will each basket have?
Each basket will have 84 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
2940/35 = 84
Problem 4
A company has 2940 widgets to be packed into 60 boxes. How many widgets will each box contain?
Each box will contain 49 widgets.
Explanation
Dividing the widgets by the total number of boxes, we will get the number of widgets in each box.
2940/60 = 49
Problem 5
A theater has 2940 seats and is divided into 98 sections. How many seats are there in each section?
Each section has 30 seats.
Explanation
Divide the total seats by the number of sections.
2940/98 = 30
FAQs on Factors of 2940
1.What are the factors of 2940?
2.Mention the prime factors of 2940.
3.Is 2940 a multiple of 7?
4.Mention the factor pairs of 2940?
5.What is the square of 2940?
6.How can children in Qatar use numbers in everyday life to understand Factors of 2940?
7.What are some fun ways kids in Qatar can practice Factors of 2940 with numbers?
8.What role do numbers and Factors of 2940 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 2940 skills?
Important Glossaries for Factor of 2940
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2940 are 1, 2, 3, 4, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 2940.
- 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 2940 are (1, 2940), (2, 1470), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the target number. For example, 14 × 210 = 2940.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 2940 is 2^2 × 3 × 5 × 7^2.
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About BrightChamps in Qatar
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.
Fun Fact
: She loves to read number jokes and games.
