100 LearnersLast updated on May 26th, 2025
Factors of 1470
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 1470, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1470?
The numbers that divide 1470 evenly are known as factors of 1470.
A factor of 1470 is a number that divides the number without remainder.
The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, and 1470.
Negative factors of 1470: -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -49, -70, -98, -105, -147, -210, -245, -294, -490, -735, and -1470.
Prime factors of 1470: 2, 3, 5, and 7.
Prime factorization of 1470: 2 × 3 × 5 × 72.
The sum of factors of 1470: 1 + 2 + 3 + 5 + 6 + 7 + 10 + 14 + 15 + 21 + 30 + 35 + 42 + 49 + 70 + 98 + 105 + 147 + 210 + 245 + 294 + 490 + 735 + 1470 = 4032
How to Find Factors of 1470?
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 1470. Identifying the numbers which are multiplied to get the number 1470 is the multiplication method.
Step 1: Multiply 1470 by 1, 1470 × 1 = 1470.
Step 2: Check for other numbers that give 1470 after multiplying
2 × 735 = 1470
3 × 490 = 1470
5 × 294 = 1470
6 × 245 = 1470
7 × 210 = 1470
10 × 147 = 1470
14 × 105 = 1470
15 × 98 = 1470
21 × 70 = 1470
30 × 49 = 1470
35 × 42 = 1470
Therefore, the positive factor pairs of 1470 are: (1, 1470), (2, 735), (3, 490), (5, 294), (6, 245), (7, 210), (10, 147), (14, 105), (15, 98), (21, 70), (30, 49), (35, 42).
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 as whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 1470 by 1, 1470 ÷ 1 = 1470.
Step 2: Continue dividing 1470 by the numbers until the remainder becomes 0.
1470 ÷ 1 = 1470
1470 ÷ 2 = 735
1470 ÷ 3 = 490
1470 ÷ 5 = 294
1470 ÷ 6 = 245
1470 ÷ 7 = 210
1470 ÷ 10 = 147
1470 ÷ 14 = 105
1470 ÷ 15 = 98
1470 ÷ 21 = 70
1470 ÷ 30 = 49
1470 ÷ 35 = 42
Therefore, the factors of 1470 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, and 1470.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 1470 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1470 ÷ 2 = 735
735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 1470 are 2, 3, 5, and 7.
The prime factorization of 1470 is: 2 × 3 × 5 × 72.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1470 is divided by 2 to get 735.
Step 2: Now divide 735 by 3 to get 245.
Step 3: Then divide 245 by 5 to get 49.
Step 4: Divide 49 by 7 to get 7.
Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1470 is: 2 × 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 1470: (1, 1470), (2, 735), (3, 490), (5, 294), (6, 245), (7, 210), (10, 147), (14, 105), (15, 98), (21, 70), (30, 49), and (35, 42).
Negative factor pairs of 1470: (-1, -1470), (-2, -735), (-3, -490), (-5, -294), (-6, -245), (-7, -210), (-10, -147), (-14, -105), (-15, -98), (-21, -70), (-30, -49), and (-35, -42).
Common Mistakes and How to Avoid Them in Factors of 1470
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 1470, 1 and 1470 are also factors.
Factors of 1470 Examples
Problem 1
A company has 1470 pencils and wants to distribute them equally among 14 employees. How many pencils will each employee get?
Each employee will get 105 pencils.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of employees.
1470/14 = 105
Problem 2
A farmer has a rectangular plot of land with a length of 49 meters and a total area of 1470 square meters. What is the width of the plot?
30 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1470 = 49 × width
To find the value of width, we need to divide the area by the length.
1470/49 = width
Width = 30.
Problem 3
There are 245 books and 7 shelves. How many books will be placed on each shelf?
Each shelf will have 35 books.
Explanation
To find the books in each shelf, divide the total books by the number of shelves.
245/7 = 35
Problem 4
In a tournament, there are 105 players and 15 teams. How many players are on each team?
There are 7 players on each team.
Explanation
Dividing the players by the total teams, we will get the number of players in each team.
105/15 = 7
Problem 5
A school has 1470 students and needs to organize them into 35 classes. How many students will be in each class?
Each class will have 42 students.
Explanation
Divide total students by the number of classes.
1470/35 = 42
FAQs on Factors of 1470
1.What are the factors of 1470?
2.Mention the prime factors of 1470.
3.Is 1470 a multiple of 14?
4.Mention the factor pairs of 1470.
5.What is the square of 1470?
Important Glossaries for Factor of 1470
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, and 1470.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 1470.
- 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 1470 are (1, 1470), (2, 735), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1470 is 2 × 3 × 5 × 72.
- Multiple: A number that can be divided by another number without a remainder. For example, 1470 is a multiple of 14.
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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.
Fun Fact
: She loves to read number jokes and games.
