102 LearnersLast updated on May 26th, 2025
Factors of 3120
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 3120, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3120?
The numbers that divide 3120 evenly are known as factors of 3120.
A factor of 3120 is a number that divides the number without remainder.
The factors of 3120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 31, 39, 40, 52, 60, 62, 65, 78, 80, 93, 104, 120, 124, 130, 156, 155, 186, 195, 208, 240, 248, 260, 310, 312, 390, 403, 465, 496, 520, 620, 624, 775, 806, 930, 1240, 1248, 1550, 1860, 2480, 3120.
Negative factors of 3120: -1, -2, -3, -4, -5, -6, -8, -10, -12, -13, -15, -16, -20, -24, -26, -30, -31, -39, -40, -52, -60, -62, -65, -78, -80, -93, -104, -120, -124, -130, -155, -156, -186, -195, -208, -240, -248, -260, -310, -312, -390, -403, -465, -496, -520, -620, -624, -775, -806, -930, -1240, -1248, -1550, -1860, -2480, -3120.
Prime factors of 3120: 2, 3, 5, and 13.
Prime factorization of 3120: 24 × 3 × 5 × 13.
The sum of factors of 3120: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 16 + 20 + 24 + 26 + 30 + 31 + 39 + 40 + 52 + 60 + 62 + 65 + 78 + 80 + 93 + 104 + 120 + 124 + 130 + 155 + 156 + 186 + 195 + 208 + 240 + 248 + 260 + 310 + 312 + 390 + 403 + 465 + 496 + 520 + 620 + 624 + 775 + 806 + 930 + 1240 + 1248 + 1550 + 1860 + 2480 + 3120 = 13632
How to Find Factors of 3120?
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 3120. Identifying the numbers which are multiplied to get the number 3120 is the multiplication method.
Step 1: Multiply 3120 by 1, 3120 × 1 = 3120.
Step 2: Check for other numbers that give 3120 after multiplying
2 × 1560 = 3120
3 × 1040 = 3120
4 × 780 = 3120
5 × 624 = 3120
6 × 520 = 3120
8 × 390 = 3120
10 × 312 = 3120
12 × 260 = 3120
13 × 240 = 3120
15 × 208 = 3120
16 × 195 = 3120
20 × 156 = 3120
24 × 130 = 3120
26 × 120 = 3120
30 × 104 = 3120
31 × 100 = 3120
39 × 80 = 3120
40 × 78 = 3120
52 × 60 = 3120
62 × 50 = 3120
Therefore, the positive factor pairs of 3120 are: (1, 3120), (2, 1560), (3, 1040), (4, 780), (5, 624), (6, 520), (8, 390), (10, 312), (12, 260), (13, 240), (15, 208), (16, 195), (20, 156), (24, 130), (26, 120), (30, 104), (31, 100), (39, 80), (40, 78), (52, 60), (62, 50). For 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 3120 by 1, 3120 ÷ 1 = 3120.
Step 2: Continue dividing 3120 by the numbers until the remainder becomes 0.
3120 ÷ 1 = 3120
3120 ÷ 2 = 1560
3120 ÷ 3 = 1040
3120 ÷ 4 = 780
3120 ÷ 5 = 624
3120 ÷ 6 = 520
3120 ÷ 8 = 390
3120 ÷ 10 = 312
3120 ÷ 12 = 260
3120 ÷ 13 = 240
3120 ÷ 15 = 208
3120 ÷ 16 = 195
3120 ÷ 20 = 156
3120 ÷ 24 = 130
3120 ÷ 26 = 120
3120 ÷ 30 = 104
3120 ÷ 31 = 100
3120 ÷ 39 = 80
120 ÷ 40 = 78
3120 ÷ 52 = 60
3120 ÷ 62 = 50
Therefore, the factors of 3120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 31, 39, 40, 52, 60, 62, 65, 78, 80, 93, 104, 120, 124, 130, 155, 156, 186, 195, 208, 240, 248, 260, 310, 312, 390, 403, 465, 496, 520, 620, 624, 775, 806, 930, 1240, 1248, 1550, 1860, 2480, 3120.
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 3120 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3120 ÷ 2 = 1560
1560 ÷ 2 = 780
780 ÷ 2 = 390
390 ÷ 2 = 195
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 3120 are 2, 3, 5, and 13.
The prime factorization of 3120 is: 2^4 × 3 × 5 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3120 is divided by 2 to get 1560.
Step 2: Now divide 1560 by 2 to get 780.
Step 3: Then divide 780 by 2 to get 390.
Step 4: Divide 390 by 2 to get 195.
Step 5: Divide 195 by 3 to get 65.
Step 6: Divide 65 by 5 to get 13.
Step 7: Finally, 13 is a prime number that cannot be divided anymore. So, the prime factorization of 3120 is: 24 × 3 × 5 × 13.
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 3120: (1, 3120), (2, 1560), (3, 1040), (4, 780), (5, 624), (6, 520), (8, 390), (10, 312), (12, 260), (13, 240), (15, 208), (16, 195), (20, 156), (24, 130), (26, 120), (30, 104), (31, 100), (39, 80), (40, 78), (52, 60), (62, 50).
Negative factor pairs of 3120: (-1, -3120), (-2, -1560), (-3, -1040), (-4, -780), (-5, -624), (-6, -520), (-8, -390), (-10, -312), (-12, -260), (-13, -240), (-15, -208), (-16, -195), (-20, -156), (-24, -130), (-26, -120), (-30, -104), (-31, -100), (-39, -80), (-40, -78), (-52, -60), (-62, -50).
Common Mistakes and How to Avoid Them in Factors of 3120
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 3120, 1 and 3120 are also factors.
Factors of 3120 Examples
Problem 1
There are 24 friends and 3120 candies. How will they divide it equally?
They will get 130 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
3120/24 = 130
Problem 2
A field is rectangular; the length of the field is 78 meters and the total area is 3120 square meters. Find the width?
40 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
3120 = 78 × width
To find the value of width, we need to shift 78 to the left side.
3120/78 = width
Width = 40.
Problem 3
There are 65 bags and 3120 apples. How many apples will be in each bag?
Each bag will have 48 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
3120/65 = 48
Problem 4
In a class, there are 3120 students, and 60 groups. How many students are there in each group?
There are 52 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
3120/60 = 52
Problem 5
3120 books need to be arranged in 52 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Explanation
Divide total books with shelves.
3120/52 = 60
FAQs on Factors of 3120
1.What are the factors of 3120?
2.Mention the prime factors of 3120.
3.Is 3120 a multiple of 4?
4.Mention the factor pairs of 3120?
5.What is the square of 3120?
6.How can children in Australia use numbers in everyday life to understand Factors of 3120?
7.What are some fun ways kids in Australia can practice Factors of 3120 with numbers?
8.What role do numbers and Factors of 3120 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 3120 skills?
Important Glossaries for Factors of 3120
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3120 are 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 3120.
- 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 3120 are (1, 3120), (2, 1560), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, 3120 can be expressed as 24 × 3 × 5 × 13.
- Multiplication method: A method used to find factor pairs by identifying numbers that multiply to give the original number. For example, identifying (2, 1560) as a factor pair of 3120.
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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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