122 LearnersLast updated on May 26th, 2025
Factors of 1410
Factors are the numbers that divide any 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 1410, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1410?
The numbers that divide 1410 evenly are known as factors of 1410.
A factor of 1410 is a number that divides the number without a remainder.
The factors of 1410 are 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, and 1410.
Negative factors of 1410: -1, -2, -3, -5, -6, -10, -15, -30, -47, -94, -141, -235, -282, -470, -705, and -1410.
Prime factors of 1410: 2, 3, 5, and 47.
Prime factorization of 1410: 2 × 3 × 5 × 47.
The sum of factors of 1410: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 47 + 94 + 141 + 235 + 282 + 470 + 705 + 1410 = 3466
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How to Find Factors of 1410?
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 1410. Identifying the numbers which are multiplied to get the number 1410 is the multiplication method.
Step 1: Multiply 1410 by 1, 1410 × 1 = 1410.
Step 2: Check for other numbers that give 1410 after multiplying
2 × 705 = 1410
3 × 470 = 1410
5 × 282 = 1410
6 × 235 = 1410
10 × 141 = 1410
15 × 94 = 1410
30 × 47 = 1410
Therefore, the positive factor pairs of 1410 are: (1, 1410), (2, 705), (3, 470), (5, 282), (6, 235), (10, 141), (15, 94), (30, 47).
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 1410 by 1, 1410 ÷ 1 = 1410.
Step 2: Continue dividing 1410 by the numbers until the remainder becomes 0.
1410 ÷ 1 = 1410
1410 ÷ 2 = 705
1410 ÷ 3 = 470
1410 ÷ 5 = 282
1410 ÷ 6 = 235
1410 ÷ 10 = 141
1410 ÷ 15 = 94
1410 ÷ 30 = 47
Therefore, the factors of 1410 are: 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, and 1410.
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 the factor tree
Using Prime Factorization: In this process, prime factors of 1410 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1410 ÷ 2 = 705 705 ÷ 3 = 235 235 ÷ 5 = 47 47 ÷ 47 = 1
The prime factors of 1410 are 2, 3, 5, and 47.
The prime factorization of 1410 is: 2 × 3 × 5 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1410 is divided by 2 to get 705.
Step 2: Now divide 705 by 3 to get 235.
Step 3: Then divide 235 by 5 to get 47. Here, 47 is a prime number, that cannot be divided anymore.
So, the prime factorization of 1410 is: 2 × 3 × 5 × 47.
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 1410: (1, 1410), (2, 705), (3, 470), (5, 282), (6, 235), (10, 141), (15, 94), and (30, 47).
Negative factor pairs of 1410: (-1, -1410), (-2, -705), (-3, -470), (-5, -282), (-6, -235), (-10, -141), (-15, -94), and (-30, -47).
Common Mistakes and How to Avoid Them in Factors of 1410
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 1410, 1 and 1410 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors, but there are also negative factors. Always check whether you have mentioned negative factors.
For example, the factors of 1410 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1410/1.5 = 940, 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 1410 are prime numbers.
For example, 2 and 3 are among the prime factors of 1410, but it has other non-prime factors like 6 and 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 1410 as 2 × 3 × 5 × 47 and missing key factors.
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Factors of 1410 Examples
Problem 1
There are 47 people and 1410 candies. How will they divide it equally?
They will get 30 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
1410/47 = 30
Problem 2
An auditorium is rectangular, the length of the auditorium is 30 meters, and the total area is 1410 square meters. Find the width?
47 meters.
Explanation
To find the width of the auditorium, we use the formula,
Area = length × width
1410 = 30 × width
To find the value of width, we need to shift 30 to the left side.
1410/30 = width
Width = 47.
Problem 3
There are 1410 marbles and 94 boxes. How many marbles will be in each box?
Each box will have 15 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1410/94 = 15
Problem 4
In a class, there are 141 students, and 10 groups. How many students are there in each group?
There are 14 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
141/10 = 14.1 (rounded to 14 for practical purposes)
Problem 5
1410 books need to be arranged in 47 shelves. How many books will go on each shelf?
Each of the shelves has 30 books.
Explanation
Divide total books by shelves.
1410/47 = 30
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FAQs on Factors of 1410
1.What are the factors of 1410?
2.Mention the prime factors of 1410.
3.Is 1410 a multiple of 5?
4.Mention the factor pairs of 1410?
5.What is the square of 1410?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 1410?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 1410 with numbers?
8.What role do numbers and Factors of 1410 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 1410 skills?
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Important Glossaries for Factor of 1410
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1410 are 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, and 1410.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 47 are prime factors of 1410.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1410 is 2 × 3 × 5 × 47.
- 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 1410 are (1, 1410), (2, 705), etc.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to give the original number. For example, for 1410, pairs like (2, 705) and (3, 470) are identified.
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About BrightChamps in United Arab Emirates
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.
