101 LearnersLast updated on May 26th, 2025
Factors of 319
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 319, how they are used in real life, and tips to learn them quickly.
What are the Factors of 319?
The numbers that divide 319 evenly are known as factors of 319.
A factor of 319 is a number that divides the number without remainder.
The factors of 319 are 1, 11, 29, and 319.
Negative factors of 319: -1, -11, -29, and -319.
Prime factors of 319: 11 and 29.
Prime factorization of 319: 11 × 29.
The sum of factors of 319: 1 + 11 + 29 + 319 = 360
How to Find Factors of 319?
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 319. Identifying the numbers which are multiplied to get the number 319 is the multiplication method.
Step 1: Multiply 319 by 1, 319 × 1 = 319.
Step 2: Check for other numbers that give 319 after multiplying 11 × 29 = 319
Therefore, the positive factor pairs of 319 are: (1, 319), (11, 29).
All these factor pairs result in 319.
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 319 by 1, 319 ÷ 1 = 319.
Step 2: Continue dividing 319 by the numbers until the remainder becomes 0.
319 ÷ 1 = 319
319 ÷ 11 = 29
Therefore, the factors of 319 are: 1, 11, 29, 319.
Prime Factors and Prime Factorization
The factors can be found by dividing them by 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 319 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
319 ÷ 11 = 29
29 ÷ 29 = 1
The prime factors of 319 are 11 and 29.
The prime factorization of 319 is: 11 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 319 is divided by 11 to get 29. Here, 29 is a prime number and cannot be divided anymore. So, the prime factorization of 319 is: 11 × 29.
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 319: (1, 319), (11, 29).
Negative factor pairs of 319: (-1, -319), (-11, -29).
Common Mistakes and How to Avoid Them in Factors of 319
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 319, 1 and 319 are also factors.
Factors of 319 Examples
Problem 1
There are 11 friends and 319 marbles. How will they divide it equally?
They will get 29 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
319/11 = 29
Problem 2
A rectangular plot has a length of 29 meters and a total area of 319 square meters. Find the width?
11 meters.
Explanation
To find the width of the plot, we use the formula, Area = length × width
319 = 29 × width
To find the value of width, we need to shift 29 to the left side.
319/29 = width
Width = 11.
Problem 3
There are 29 shelves and 319 books. How many books will be in each shelf?
Each shelf will have 11 books.
Explanation
To find the books in each shelf, divide the total books by the number of shelves.
319/29 = 11
Problem 4
In a seminar, there are 319 participants, and 11 groups. How many participants are there in each group?
There are 29 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
319/11 = 29
Problem 5
319 apples need to be arranged in 11 boxes. How many apples will go in each box?
Each box will have 29 apples.
Explanation
Divide total apples by the number of boxes.
319/11 = 29
FAQs on Factors of 319
1.What are the factors of 319?
2.Mention the prime factors of 319.
3.Is 319 a multiple of 11?
4.Mention the factor pairs of 319?
5.What is the square of 319?
6.How can children in Canada use numbers in everyday life to understand Factors of 319?
7.What are some fun ways kids in Canada can practice Factors of 319 with numbers?
8.What role do numbers and Factors of 319 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 319 skills?
Important Glossaries for Factor of 319
- Factors: The numbers that divide the given number without leaving a remainder. For example, the factors of 319 are 1, 11, 29, and 319.
- Prime factors: The factors which are prime numbers. For example, 11 and 29 are prime factors of 319.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number. For example, the factor pairs of 319 are (1, 319), (11, 29).
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.
- Division method: A method to find factors by dividing the given number by whole numbers to check for zero remainders.
Explore More numbers
Previous to Factors of 319
About BrightChamps in Canada
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.
