117 LearnersLast updated on May 26th, 2025
Factors of 1785
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1785, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1785?
The numbers that divide 1785 evenly are known as factors of 1785.
A factor of 1785 is a number that divides the number without remainder.
The factors of 1785 are 1, 3, 5, 15, 119, 357, 595, and 1785.
Negative factors of 1785: -1, -3, -5, -15, -119, -357, -595, and -1785.
Prime factors of 1785: 3, 5, and 119.
Prime factorization of 1785: 3 × 5 × 119.
The sum of factors of 1785: 1 + 3 + 5 + 15 + 119 + 357 + 595 + 1785 = 2880
How to Find Factors of 1785?
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 1785. Identifying the numbers which are multiplied to get the number 1785 is the multiplication method.
Step 1: Multiply 1785 by 1, 1785 × 1 = 1785.
Step 2: Check for other numbers that give 1785 after multiplying
3 × 595 = 1785
5 × 357 = 1785
15 × 119 = 1785
Therefore, the positive factor pairs of 1785 are: (1, 1785), (3, 595), (5, 357), (15, 119).
All these factor pairs result in 1785.
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 simple division method -
Step 1: Divide 1785 by 1, 1785 ÷ 1 = 1785.
Step 2: Continue dividing 1785 by the numbers until the remainder becomes 0.
1785 ÷ 1 = 1785
1785 ÷ 3 = 595
1785 ÷ 5 = 357
1785 ÷ 15 = 119
Therefore, the factors of 1785 are: 1, 3, 5, 15, 119, 357, 595, 1785.
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 1785 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1785 ÷ 3 = 595
595 ÷ 5 = 119
119 is a product of two primes, 7 and 17.
The prime factors of 1785 are 3, 5, 7, and 17.
The prime factorization of 1785 is: 3 × 5 × 7 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1785 is divided by 3 to get 595.
Step 2: Now divide 595 by 5 to get 119.
Step 3: 119 can be further divided by 7 to get 17.
Here, 17 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1785 is: 3 × 5 × 7 × 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 1785: (1, 1785), (3, 595), (5, 357), and (15, 119).
Negative factor pairs of 1785: (-1, -1785), (-3, -595), (-5, -357), and (-15, -119).
Common Mistakes and How to Avoid Them in Factors of 1785
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1785, 1 and 1785 are also factors.
Factors of 1785 Examples
Problem 1
There are 3 friends and 1785 marbles. How will they divide it equally?
They will get 595 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
1785/3 = 595
Problem 2
A garden is rectangular, the length of the garden is 15 meters and the total area is 1785 square meters. Find the width?
119 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1785 = 15 × width
To find the value of width, we need to shift 15 to the left side.
1785/15 = width
Width = 119.
Problem 3
There are 5 baskets and 1785 apples. How many apples will be in each basket?
Each basket will have 357 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1785/5 = 357
Problem 4
In a conference, there are 1785 attendees, and 15 groups. How many attendees are there in each group?
There are 119 attendees in each group.
Explanation
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1785/15 = 119
Problem 5
1785 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 357 books.
Explanation
Divide total books by shelves.
1785/5 = 357
FAQs on Factors of 1785
1.What are the factors of 1785?
2.Mention the prime factors of 1785.
3.Is 1785 a multiple of 15?
4.Mention the factor pairs of 1785?
5.What is the square of 1785?
6.How can children in United States use numbers in everyday life to understand Factors of 1785?
7.What are some fun ways kids in United States can practice Factors of 1785 with numbers?
8.What role do numbers and Factors of 1785 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1785 skills?
Important Glossaries for Factor of 1785
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1785 are 1, 3, 5, 15, 119, 357, 595, and 1785.
- Prime factors: The factors which are prime numbers. For example, 3, 5, 7, and 17 are prime factors of 1785.
- 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 1785 are (1, 1785), (3, 595), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 1785 is 3 × 5 × 7 × 17.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1785 is a multiple of 15.
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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
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