123 LearnersLast updated on May 26th, 2025
Factors of 1725
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 1725, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1725?
The numbers that divide 1725 evenly are known as factors of 1725.
A factor of 1725 is a number that divides the number without remainder.
The factors of 1725 are 1, 3, 5, 15, 23, 69, 115, 345, 575, and 1725.
Negative factors of 1725: -1, -3, -5, -15, -23, -69, -115, -345, -575, and -1725.
Prime factors of 1725: 3, 5, and 23.
Prime factorization of 1725: 3 × 5 × 23.
The sum of factors of 1725: 1 + 3 + 5 + 15 + 23 + 69 + 115 + 345 + 575 + 1725 = 2876
How to Find Factors of 1725?
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 1725. Identifying the numbers which are multiplied to get the number 1725 is the multiplication method.
Step 1: Multiply 1725 by 1, 1725 × 1 = 1725.
Step 2: Check for other numbers that give 1725 after multiplying
3 × 575 = 1725
5 × 345 = 1725
15 × 115 = 1725
23 × 75 = 1725
Therefore, the positive factor pairs of 1725 are: (1, 1725), (3, 575), (5, 345), (15, 115), (23, 75).
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 the simple division method
Step 1: Divide 1725 by 1, 1725 ÷ 1 = 1725.
Step 2: Continue dividing 1725 by the numbers until the remainder becomes 0.
1725 ÷ 1 = 1725
1725 ÷ 3 = 575
1725 ÷ 5 = 345
1725 ÷ 15 = 115
1725 ÷ 23 = 75
Therefore, the factors of 1725 are: 1, 3, 5, 15, 23, 69, 115, 345, 575, 1725.
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 1725 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1725 ÷ 3 = 575
575 ÷ 5 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1
The prime factors of 1725 are 3, 5, and 23.
The prime factorization of 1725 is: 3 × 5 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1725 is divided by 3 to get 575.
Step 2: Now divide 575 by 5 to get 115. Step 3: Then divide 115 by 5 to get 23. Here, 23 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1725 is: 3 × 5 × 23.
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 1725: (1, 1725), (3, 575), (5, 345), (15, 115), and (23, 75).
Negative factor pairs of 1725: (-1, -1725), (-3, -575), (-5, -345), (-15, -115), and (-23, -75).
Common Mistakes and How to Avoid Them in Factors of 1725
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 1725, 1 and 1725 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 1725 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1725/1.5 = 1150, 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 1725 are prime numbers.
For example, 3, 5, and 23 are the prime factors of 1725, but it has other factors like 15, 69.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1725 as 3 × 5 × 23 and missing all the key factors.
Factors of 1725 Examples
Problem 1
There are 3 teams and 1725 points. How will they distribute the points equally?
Each team will get 575 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
1725/3 = 575
Problem 2
A garden is rectangular, the length of the garden is 23 meters, and the total area is 1725 square meters. Find the width?
75 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1725 = 23 × width
To find the value of width, we need to shift 23 to the left side.
1725/23 = width
Width = 75.
Problem 3
There are 5 baskets and 1725 apples. How many apples will be in each basket?
Each basket will have 345 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
1725/5 = 345
Problem 4
In a conference, there are 115 participants, and 15 groups. How many participants are there in each group?
There are 7 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
115/15 = 7
Problem 5
1725 files need to be arranged in 23 folders. How many files will go in each folder?
Each folder will have 75 files.
Explanation
Divide total files by the number of folders.
1725/23 = 75
FAQs on Factors of 1725
1.What are the factors of 1725?
2.Mention the prime factors of 1725.
3.Is 1725 a multiple of 23?
4.Mention the factor pairs of 1725?
5.What is the square of 1725?
6.How can children in Canada use numbers in everyday life to understand Factors of 1725?
7.What are some fun ways kids in Canada can practice Factors of 1725 with numbers?
8.What role do numbers and Factors of 1725 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1725 skills?
Important Glossaries for Factor of 1725
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1725 are 1, 3, 5, 15, 23, 69, 115, 345, 575, and 1725.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 23 are prime factors of 1725.
- 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 1725 are (1, 1725), (3, 575), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1725 is 3 × 5 × 23.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number. For example, 3 × 575 = 1725.
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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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