124 LearnersLast updated on May 26th, 2025
Factors of 1419
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 1419, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1419?
The numbers that divide 1419 evenly are known as factors of 1419.
A factor of 1419 is a number that divides the number without remainder.
The factors of 1419 are 1, 3, 11, 33, 43, 129, 473, and 1419.
Negative factors of 1419: -1, -3, -11, -33, -43, -129, -473, and -1419.
Prime factors of 1419: 3, 11, and 43.
Prime factorization of 1419: 3 × 11 × 43.
The sum of factors of 1419: 1 + 3 + 11 + 33 + 43 + 129 + 473 + 1419 = 2112
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How to Find Factors of 1419?
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 1419. Identifying the numbers which are multiplied to get the number 1419 is the multiplication method.
Step 1: Multiply 1419 by 1, 1419 × 1 = 1419.
Step 2: Check for other numbers that give 1419 after multiplying
3 × 473 = 1419
11 × 129 = 1419
33 × 43 = 1419
Therefore, the positive factor pairs of 1419 are: (1, 1419), (3, 473), (11, 129), (33, 43).
All these factor pairs result in 1419.
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 1419 by 1, 1419 ÷ 1 = 1419.
Step 2: Continue dividing 1419 by the numbers until the remainder becomes 0.
1419 ÷ 1 = 1419
1419 ÷ 3 = 473
1419 ÷ 11 = 129
1419 ÷ 33 = 43
Therefore, the factors of 1419 are: 1, 3, 11, 33, 43, 129, 473, and 1419.
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 1419 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1419 ÷ 3 = 473
473 ÷ 11 = 43
43 ÷ 43 = 1
The prime factors of 1419 are 3, 11, and 43.
The prime factorization of 1419 is: 3 × 11 × 43.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1419 is divided by 3 to get 473.
Step 2: Now divide 473 by 11 to get 43.
Step 3: Here, 43 is a prime number and cannot be divided anymore.
So, the prime factorization of 1419 is: 3 × 11 × 43.
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 1419: (1, 1419), (3, 473), (11, 129), and (33, 43).
Negative factor pairs of 1419: (-1, -1419), (-3, -473), (-11, -129), and (-33, -43).
Common Mistakes and How to Avoid Them in Factors of 1419
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1419, 1 and 1419 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 1419 consist of -1, -3, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 7.5 as a factor, because 1419/7.5 = 189.2, 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 1419 are prime numbers.
For example, 3, 11, and 43 are the prime factors of 1419, but it has other factors like 33, 129.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1419 as 3 × 11 × 43 and missing all the key factors.
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Factors of 1419 Examples
Problem 1
There are 1419 apples and 3 baskets. How will they divide it equally?
They will get 473 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
1419/3 = 473
Problem 2
A rectangular garden has a length of 11 meters and the total area is 1419 square meters. Find the width.
129 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1419 = 11 × width
To find the value of width, we need to shift 11 to the left side.
1419/11 = width
Width = 129.
Problem 3
There are 33 teachers and 1419 students. How many students per teacher?
Each teacher will have 43 students.
Explanation
To find the students per teacher, divide the total students by the number of teachers.
1419/33 = 43
Problem 4
In a library, there are 1419 books and 11 shelves. How many books are there on each shelf?
There are 129 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
1419/11 = 129
Problem 5
A company has 1419 employees and 3 departments. How many employees are in each department?
Each department has 473 employees.
Explanation
Divide the total employees by the number of departments.
1419/3 = 473
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FAQs on Factors of 1419
1.What are the factors of 1419?
2.Mention the prime factors of 1419.
3.Is 1419 a multiple of 11?
4.Mention the factor pairs of 1419?
5.What is the square of 1419?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1419?
7.What are some fun ways kids in United Kingdom can practice Factors of 1419 with numbers?
8.What role do numbers and Factors of 1419 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1419 skills?
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Important Glossaries for Factor of 1419
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1419 are 1, 3, 11, 33, 43, 129, 473, and 1419.
- Prime factors: The factors which are prime numbers. For example, 3, 11, and 43 are prime factors of 1419.
- 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 1419 are (1, 1419), (3, 473), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1419 is 3 × 11 × 43.
- Negative factors: Negative numbers that divide the original number without leaving a remainder. For example, the negative factors of 1419 are -1, -3, -11, -33, -43, -129, -473, and -1419.
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Hiralee Lalitkumar Makwana
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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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