127 LearnersLast updated on May 26th, 2025
Factors of 1407
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 1407, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1407?
The numbers that divide 1407 evenly are known as factors of 1407.
A factor of 1407 is a number that divides the number without remainder.
The factors of 1407 are 1, 3, 469, and 1407.
Negative factors of 1407: -1, -3, -469, and -1407.
Prime factors of 1407: 3 and 469.
Prime factorization of 1407: 3 × 469.
The sum of factors of 1407: 1 + 3 + 469 + 1407 = 1880
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How to Find Factors of 1407?
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 1407. Identifying the numbers which are multiplied to get the number 1407 is the multiplication method.
Step 1: Multiply 1407 by 1, 1407 × 1 = 1407.
Step 2: Check for other numbers that give 1407 after multiplying
3 × 469 = 1407
Therefore, the positive factor pairs of 1407 are: (1, 1407) and (3, 469).
All these factor pairs result in 1407.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 1407 by 1, 1407 ÷ 1 = 1407.
Step 2: Continue dividing 1407 by the numbers until the remainder becomes 0.
1407 ÷ 1 = 1407
1407 ÷ 3 = 469
Therefore, the factors of 1407 are: 1, 3, 469, and 1407.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1407 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1407 ÷ 3 = 469 469 is a prime number.
The prime factors of 1407 are 3 and 469.
The prime factorization of 1407 is: 3 × 469.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1407 is divided by 3 to get 469.
Step 2: 469 is a prime number and cannot be divided further.
So, the prime factorization of 1407 is: 3 × 469.
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 1407: (1, 1407) and (3, 469).
Negative factor pairs of 1407: (-1, -1407) and (-3, -469).
Common Mistakes and How to Avoid Them in Factors of 1407
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 1407, 1 and 1407 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1407 include -1, -3, -469, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 1407/1.5 = 938, which 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 1407 are prime numbers.
For example, 3 and 469 are the prime factors of 1407, but it has other factors like 1, 1407.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1407 as 3 × 469 and missing all the key factors.
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Factors of 1407 Examples
Problem 1
A basketball team scored 1407 points in a season, and they played 469 games. How many points did they average per game?
They averaged 3 points per game.
Explanation
To find the average points per game, divide the total points by the number of games.
1407/469 = 3
Problem 2
A farmer has 1407 apples and wants to pack them into 3 baskets equally. How many apples will each basket have?
Each basket will have 469 apples.
Explanation
To divide apples equally, use the equation:
1407/3 = 469
Problem 3
A library has 1407 books and 3 sections. How many books will each section have?
Each section will have 469 books.
Explanation
Divide the total number of books by the number of sections.
1407/3 = 469
Problem 4
A company produced 1407 units of a product and sold them in 469 stores. How many units were sold per store?
3 units were sold per store.
Explanation
Dividing the total units by the number of stores gives the units per store.
1407/469 = 3
Problem 5
There are 3 teams in a competition with a total of 1407 points. How many points does each team get if they are equally distributed?
Each team gets 469 points.
Explanation
To find the points per team, divide the total points by the number of teams.
1407/3 = 469
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FAQs on Factors of 1407
1.What are the factors of 1407?
2.Mention the prime factors of 1407.
3.Is 1407 a multiple of 3?
4.Mention the factor pairs of 1407?
5.What is the square of 1407?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1407?
7.What are some fun ways kids in Qatar can practice Factors of 1407 with numbers?
8.What role do numbers and Factors of 1407 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1407 skills?
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Important Glossaries for Factors of 1407
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1407 are 1, 3, 469, and 1407.
- Prime factors: The factors which are prime numbers. For example, 3 and 469 are prime factors of 1407.
- 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 1407 are (1, 1407) and (3, 469).
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, 1407 can be expressed as 3 × 469.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1407 is a multiple of 3.
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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.
