118 LearnersLast updated on May 26th, 2025
Factors of 219
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 219, how they are used in real life, and tips to learn them quickly.
What are the Factors of 219?
The numbers that divide 219 evenly are known as factors of 219.
A factor of 219 is a number that divides the number without a remainder.
The factors of 219 are 1, 3, 73, and 219.
Negative factors of 219: -1, -3, -73, and -219.
Prime factors of 219: 3 and 73.
Prime factorization of 219: 3 × 73.
The sum of factors of 219: 1 + 3 + 73 + 219 = 296
How to Find Factors of 219?
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 219. Identifying the numbers which are multiplied to get the number 219 is the multiplication method.
Step 1: Multiply 219 by 1, 219 × 1 = 219.
Step 2: Check for other numbers that give 219 after multiplying
3 × 73 = 219
Therefore, the positive factor pairs of 219 are: (1, 219) and (3, 73).
All these factor pairs result in 219.
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 219 by 1, 219 ÷ 1 = 219.
Step 2: Continue dividing 219 by the numbers until the remainder becomes 0.
219 ÷ 1 = 219
219 ÷ 3 = 73
Therefore, the factors of 219 are: 1, 3, 73, and 219.
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 219 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
219 ÷ 3 = 73
73 ÷ 73 = 1
The prime factors of 219 are 3 and 73.
The prime factorization of 219 is: 3 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 219 is divided by 3 to get 73.
Step 2: Now divide 73 by 73 to get 1.
Here, 73 is a prime number and cannot be divided further.
So, the prime factorization of 219 is: 3 × 73.
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 219: (1, 219) and (3, 73).
Negative factor pairs of 219: (-1, -219) and (-3, -73).
Common Mistakes and How to Avoid Them in Factors of 219
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 219, 1 and 219 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 219 consist of -1, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 219/1.5 = 146, 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 219 are prime numbers.
For example, 3 and 73 are the prime factors of 219, but it has other factors like 1 and 219.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 219 as 3 × 73 and missing all the key factors.
Factors of 219 Examples
Problem 1
There are 3 teams and 219 participants in a competition. How will they divide the participants equally?
Each team will have 73 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
219/3 = 73
Problem 2
A runner completes a distance of 219 meters in 3 equal laps. How long is each lap?
Each lap is 73 meters.
Explanation
To find the length of each lap, we use the formula, Total distance = number of laps × length of each lap
219 = 3 × length of each lap
To find the value of each lap, we need to shift 3 to the left side.
219/3 = length of each lap
Length of each lap = 73.
Problem 3
There are 219 apples and 73 baskets. How many apples will be in each basket?
Each basket will have 3 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
219/73 = 3
Problem 4
In a conference, there are 219 attendees and 3 rooms. How many attendees are there in each room?
There are 73 attendees in each room.
Explanation
Dividing the attendees by the total rooms, we will get the number of attendees in each room.
219/3 = 73
Problem 5
219 books need to be arranged in 73 shelves. How many books will go on each shelf?
Each of the shelves has 3 books.
Explanation
Divide total books by shelves.
219/73 = 3
FAQs on Factors of 219
1.What are the factors of 219?
2.Mention the prime factors of 219.
3.Is 219 a multiple of 3?
4.Mention the factor pairs of 219?
5.What is the square of 219?
6.How can children in Singapore use numbers in everyday life to understand Factors of 219?
7.What are some fun ways kids in Singapore can practice Factors of 219 with numbers?
8.What role do numbers and Factors of 219 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of 219 skills?
Important Glossaries for Factor of 219
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 219 are 1, 3, 73, and 219.
- Prime factors: The factors which are prime numbers. For example, 3 and 73 are prime factors of 219.
- 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 219 are (1, 219) and (3, 73).
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 219 is 3 × 73.
- Multiple: A number that can be divided by another number without a remainder. For example, 219 is a multiple of 3.
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About BrightChamps in Singapore
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.
