102 LearnersLast updated on May 26th, 2025
Factors of 1708
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 1708, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1708?
The numbers that divide 1708 evenly are known as factors of 1708.
A factor of 1708 is a number that divides the number without remainder.
The factors of 1708 are 1, 2, 4, 11, 22, 31, 34, 62, 68, 124, 341, 682, 1708.
Negative factors of 1708: -1, -2, -4, -11, -22, -31, -34, -62, -68, -124, -341, -682, -1708.
Prime factors of 1708: 2, 11, and 31.
Prime factorization of 1708: 2 × 2 × 11 × 31.
The sum of factors of 1708: 1 + 2 + 4 + 11 + 22 + 31 + 34 + 62 + 68 + 124 + 341 + 682 + 1708 = 3090.
How to Find Factors of 1708?
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 1708. Identifying the numbers which are multiplied to get the number 1708 is the multiplication method.
Step 1: Multiply 1708 by 1, 1708 × 1 = 1708.
Step 2: Check for other numbers that give 1708 after multiplying:
2 × 854 = 1708
4 × 427 = 1708
11 × 155 = 1708
22 × 77 = 1708
31 × 55 = 1708
Therefore, the positive factor pairs of 1708 are: (1, 1708), (2, 854), (4, 427), (11, 155), (22, 77), (31, 55).
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 1708 by 1, 1708 ÷ 1 = 1708.
Step 2: Continue dividing 1708 by the numbers until the remainder becomes 0.
1708 ÷ 1 = 1708
1708 ÷ 2 = 854
1708 ÷ 4 = 427
1708 ÷ 11 = 155
1708 ÷ 22 = 77
1708 ÷ 31 = 55
Therefore, the factors of 1708 are: 1, 2, 4, 11, 22, 31, 34, 62, 68, 124, 341, 682, 1708.
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 1708 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1708 ÷ 2 = 854
854 ÷ 2 = 427
427 ÷ 11 = 38.818 (not a whole number, so try next prime)
427 ÷ 31 = 13.774 (not a whole number, so check again)
We see that 427 is actually prime, so the factorization stops there.
The prime factors of 1708 are 2, 11, and 31.
The prime factorization of 1708 is: 2 × 2 × 11 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1708 is divided by 2 to get 854.
Step 2: Now divide 854 by 2 to get 427.
Step 3: 427 is a prime number, so it cannot be divided further. So, the prime factorization of 1708 is: 2 × 2 × 11 × 31.
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 1708: (1, 1708), (2, 854), (4, 427), (11, 155), (22, 77), (31, 55).
Negative factor pairs of 1708: (-1, -1708), (-2, -854), (-4, -427), (-11, -155), (-22, -77), (-31, -55).
Common Mistakes and How to Avoid Them in Factors of 1708
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 1708, 1 and 1708 are also factors.
Factors of 1708 Examples
Problem 1
There are 22 students and 1708 apples. How will they distribute them equally?
They will get 77 apples each.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of students.
1708/22 = 77
Problem 2
A painting is rectangular, the length of the painting is 31 inches, and the total area is 1708 square inches. Find the width.
55 inches.
Explanation
To find the width of the painting, we use the formula,
Area = length × width
1708 = 31 × width
To find the value of width, we need to shift 31 to the left side.
1708/31 = width
Width = 55.
Problem 3
There are 11 gift boxes and 1708 candies. How many candies will be in each box?
Each gift box will have 155 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
1708/11 = 155
Problem 4
In a conference, there are 1708 participants and 2 halls. How many participants are there in each hall?
There are 854 participants in each hall.
Explanation
Dividing the participants by the total halls, we will get the number of participants in each hall.
1708/2 = 854
Problem 5
1708 books need to be arranged in 4 sections. How many books will go in each section?
Each of the sections has 427 books.
Explanation
Divide the total books by the sections.
1708/4 = 427
FAQs on Factors of 1708
1.What are the factors of 1708?
2.Mention the prime factors of 1708.
3.Is 1708 a multiple of 11?
4.Mention the factor pairs of 1708?
5.What is the square of 1708?
Important Glossaries for Factors of 1708
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1708 are 1, 2, 4, 11, 22, 31, 34, 62, 68, 124, 341, 682, and 1708.
- Prime factors: The factors which are prime numbers. For example, 2, 11, and 31 are prime factors of 1708.
- 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 1708 are (1, 1708), (2, 854), etc.
- Prime factorization: The process of determining the prime numbers that multiply together to give a specific original number. For 1708, it is 2 × 2 × 11 × 31.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to yield the target number. For example, finding pairs for 1708 using multiplication.
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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.
