122 LearnersLast updated on May 26th, 2025
Factors of 1700
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 1700, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1700?
The numbers that divide 1700 evenly are known as factors of 1700.
A factor of 1700 is a number that divides the number without remainder.
The factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, and 1700.
Negative factors of 1700: -1, -2, -4, -5, -10, -17, -20, -25, -34, -50, -68, -85, -100, -170, -340, -425, -850, and -1700.
Prime factors of 1700: 2, 5, and 17.
Prime factorization of 1700: 2² × 5² × 17.
The sum of factors of 1700: 1 + 2 + 4 + 5 + 10 + 17 + 20 + 25 + 34 + 50 + 68 + 85 + 100 + 170 + 340 + 425 + 850 + 1700 = 3916
How to Find Factors of 1700?
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 1700. Identifying the numbers which are multiplied to get the number 1700 is the multiplication method.
Step 1: Multiply 1700 by 1, 1700 × 1 = 1700.
Step 2: Check for other numbers that give 1700 after multiplying
2 × 850 = 1700
4 × 425 = 1700
5 × 340 = 1700
10 × 170 = 1700
17 × 100 = 1700
20 × 85 = 1700
25 × 68 = 1700
34 × 50 = 1700
Therefore, the positive factor pairs of 1700 are: (1, 1700), (2, 850), (4, 425), (5, 340), (10, 170), (17, 100), (20, 85), (25, 68), and (34, 50).
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 1700 by 1, 1700 ÷ 1 = 1700.
Step 2: Continue dividing 1700 by the numbers until the remainder becomes 0.
1700 ÷ 1 = 1700
1700 ÷ 2 = 850
1700 ÷ 4 = 425
1700 ÷ 5 = 340
1700 ÷ 10 = 170
1700 ÷ 17 = 100
1700 ÷ 20 = 85
1700 ÷ 25 = 68
1700 ÷ 34 = 50
Therefore, the factors of 1700 are: 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1700 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1700 ÷ 2 = 850
850 ÷ 2 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 1700 are 2, 5, and 17.
The prime factorization of 1700 is: 2² × 5² × 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, 1700 is divided by 2 to get 850.
Step 2: Now divide 850 by 2 to get 425.
Step 3: Then divide 425 by 5 to get 85.
Step 4: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1700 is: 2² × 5² × 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 1700: (1, 1700), (2, 850), (4, 425), (5, 340), (10, 170), (17, 100), (20, 85), (25, 68), (34, 50).
Negative factor pairs of 1700: (-1, -1700), (-2, -850), (-4, -425), (-5, -340), (-10, -170), (-17, -100), (-20, -85), (-25, -68), (-34, -50).
Common Mistakes and How to Avoid Them in Factors of 1700
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 1700, 1 and 1700 is also a factor.
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 1700 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1700/1.5 = 1133.333, 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 1700 are prime numbers.
For example, 2, 5, and 17 are the prime factors of 1700, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, Not breaking 1700 as 2² × 5² × 17 and missing all the key factors.
Factors of 1700 Examples
Problem 1
There are 34 students and 1700 candies. How will they divide it equally?
They will get 50 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
1700/34 = 50
Problem 2
A rectangular plot has a length of 25 meters and a total area of 1700 square meters. Find the width?
68 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1700 = 25 × width
To find the value of width, we need to shift 25 to the left side.
1700/25 = width
Width = 68.
Problem 3
There are 85 boxes and 1700 marbles. How many marbles will be in each box?
Each box will have 20 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
1700/85 = 20
Problem 4
In a school, there are 1700 students, and 50 classes. How many students are there in each class?
There are 34 students in each class.
Explanation
Dividing the students with the total classes, we will get the number of students in each class.
1700/50 = 34
Problem 5
1700 apples need to be packed in 100 baskets. How many apples will go in each basket?
Each of the baskets has 17 apples.
Explanation
Divide total apples with baskets.
1700/100 = 17
FAQs on Factors of 1700
1.What are the factors of 1700?
2.Mention the prime factors of 1700.
3.Is 1700 a multiple of 4?
4.Mention the factor pairs of 1700?
5.What is the square of 1700?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1700?
7.What are some fun ways kids in United Kingdom can practice Factors of 1700 with numbers?
8.What role do numbers and Factors of 1700 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1700 skills?
Important Glossaries for Factor of 1700
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, and 1700.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 1700.
- 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 1700 are (1, 1700), (2, 850), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1700 is 2² × 5² × 17.
- Multiple: A number that can be divided by another number without a remainder. For example, 1700 is a multiple of 4.
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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
: She loves to read number jokes and games.
