101 LearnersLast updated on May 26th, 2025
Factors of 1360
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 1360, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1360?
The numbers that divide 1360 evenly are known as factors of 1360.
A factor of 1360 is a number that divides the number without remainder.
The factors of 1360 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680, and 1360.
Negative factors of 1360: -1, -2, -4, -5, -8, -10, -16, -17, -20, -34, -40, -68, -80, -85, -136, -170, -272, -340, -680, and -1360.
Prime factors of 1360: 2, 5, and 17.
Prime factorization of 1360: 24 × 5 × 17.
The sum of factors of 1360: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 17 + 20 + 34 + 40 + 68 + 80 + 85 + 136 + 170 + 272 + 340 + 680 + 1360 = 2708
How to Find Factors of 1360?
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 1360. Identifying the numbers which are multiplied to get the number 1360 is the multiplication method.
Step 1: Multiply 1360 by 1, 1360 × 1 = 1360.
Step 2: Check for other numbers that give 1360 after multiplying
2 × 680 = 1360
4 × 340 = 1360
5 × 272 = 1360
8 × 170 = 1360
10 × 136 = 1360
16 × 85 = 1360
17 × 80 = 1360
20 × 68 = 1360
34 × 40 = 1360
Therefore, the positive factor pairs of 1360 are: (1, 1360), (2, 680), (4, 340), (5, 272), (8, 170), (10, 136), (16, 85), (17, 80), (20, 68), (34, 40).
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 1360 by 1, 1360 ÷ 1 = 1360.
Step 2: Continue dividing 1360 by the numbers until the remainder becomes 0.
1360 ÷ 1 = 1360
1360 ÷ 2 = 680
1360 ÷ 4 = 340
1360 ÷ 5 = 272
1360 ÷ 8 = 170
1360 ÷ 10 = 136
1360 ÷ 16 = 85
1360 ÷ 17 = 80
1360 ÷ 20 = 68
1360 ÷ 34 = 40
Therefore, the factors of 1360 are: 1, 2, 4, 5, 8, 10, 16, 17, 20, 34, 40, 68, 80, 85, 136, 170, 272, 340, 680, 1360.
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 1360 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1360 ÷ 2 = 680
680 ÷ 2 = 340
340 ÷ 2 = 170
170 ÷ 2 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 1360 are 2, 5, and 17.
The prime factorization of 1360 is: 24 × 5 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1360 is divided by 2 to get 680.
Step 2: Now divide 680 by 2 to get 340.
Step 3: Then divide 340 by 2 to get 170.
Step 4: Divide 170 by 2 to get 85.
Step 5: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1360 is: 24 × 5 × 17.
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 1360: (1, 1360), (2, 680), (4, 340), (5, 272), (8, 170), (10, 136), (16, 85), (17, 80), (20, 68), (34, 40).
Negative factor pairs of 1360: (-1, -1360), (-2, -680), (-4, -340), (-5, -272), (-8, -170), (-10, -136), (-16, -85), (-17, -80), (-20, -68), (-34, -40).
Common Mistakes and How to Avoid Them in Factors of 1360
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1360, 1 and 1360 are also factors.
Factors of 1360 Examples
Problem 1
There are 8 teams and 1360 points. How will they distribute the points equally?
They will get 170 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
1360/8 = 170
Problem 2
A rectangular garden has a length of 40 meters and a total area of 1360 square meters. Find the width.
34 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1360 = 40 × width
To find the value of width, we need to shift 40 to the left side.
1360/40 = width
Width = 34.
Problem 3
There are 85 gift bags and 1360 candies. How many candies will be in each bag?
Each bag will have 16 candies.
Explanation
To find the candies in each bag, divide the total candies by the number of bags.
1360/85 = 16
Problem 4
In a conference, there are 1360 participants and 17 breakout rooms. How many participants are there in each room?
There are 80 participants in each room.
Explanation
Dividing the participants by the total rooms, we will get the number of participants in each room.
1360/17 = 80
Problem 5
A library has 272 books to be arranged in 5 sections. How many books will go in one section?
Each section will have 54 books.
Explanation
Divide total books by sections.
272/5 = 54.4 (Since books cannot be split, adjust the distribution accordingly in practical cases.)
FAQs on Factors of 1360
1.What are the factors of 1360?
2.Mention the prime factors of 1360.
3.Is 1360 a multiple of 10?
4.Mention the factor pairs of 1360.
5.What is the square of 1360?
6.How can children in Australia use numbers in everyday life to understand Factors of 1360?
7.What are some fun ways kids in Australia can practice Factors of 1360 with numbers?
8.What role do numbers and Factors of 1360 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 1360 skills?
Important Glossaries for Factors of 1360
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1360 are 1, 2, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 1360.
- 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 1360 are (1, 1360), (2, 680), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1360 is 2^4 × 5 × 17.
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to give the original number. For example, 2 × 680 = 1360.
Explore More numbers
Previous to Factors of 1360
About BrightChamps in Australia
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.
