101 LearnersLast updated on May 26th, 2025
Factors of 1694
Factors are the numbers that divide any given number evenly without a 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 1694, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1694?
The numbers that divide 1694 evenly are known as factors of 1694.
A factor of 1694 is a number that divides the number without remainder.
The factors of 1694 are 1, 2, 3, 6, 13, 26, 29, 39, 58, 78, 87, 174, 169, 338, 507, 846, and 1694.
Negative factors of 1694: -1, -2, -3, -6, -13, -26, -29, -39, -58, -78, -87, -174, -169, -338, -507, -846, and -1694.
Prime factors of 1694: 2, 3, and 169.
Prime factorization of 1694: 2 × 3 × 169.
The sum of factors of 1694: 1 + 2 + 3 + 6 + 13 + 26 + 29 + 39 + 58 + 78 + 87 + 174 + 169 + 338 + 507 + 846 + 1694 = 4070
How to Find Factors of 1694?
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 1694. Identifying the numbers which are multiplied to get the number 1694 is the multiplication method.
Step 1: Multiply 1694 by 1, 1694 × 1 = 1694.
Step 2: Check for other numbers that give 1694 after multiplying:
2 × 847 = 1694
3 × 564.67 (since 564.67 is not a whole number, 3 is not a factor)
13 × 130.3 (since 130.3 is not a whole number, 13 is not a factor)
29 × 58.41 (since 58.41 is not a whole number, 29 is not a factor)
Therefore, the positive factor pairs of 1694 are: (1, 1694), (2, 847).
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 in whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 1694 by 1, 1694 ÷ 1 = 1694.
Step 2: Continue dividing 1694 by the numbers until the remainder becomes 0.
1694 ÷ 1 = 1694
1694 ÷ 2 = 847
1694 ÷ 3 = 564.67 (not a factor)
1694 ÷ 6 = 282.33 (not a factor)
Therefore, the factors of 1694 are: 1, 2, 13, 26, 29, 58, 169, 338, 847, 1694.
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 1694 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1694 ÷ 2 = 847
847 ÷ 13 = 65.15 (not a factor)
1694 ÷ 3 = 564.67 (not a factor)
The prime factors of 1694 are 2, 3, and 169.
The prime factorization of 1694 is: 2 × 3 × 169.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1694 is divided by 2 to get 847.
Step 2: Now divide 847 by 3 to get 282.33 (not a factor). Step 3: Divide 847 by 13 to get 65.15 (not a factor). Here, the smallest prime number, 169, cannot be divided anymore. So, the prime factorization of 1694 is: 2 × 3 × 169.
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 1694: (1, 1694), (2, 847).
Negative factor pairs of 1694: (-1, -1694), (-2, -847).
Common Mistakes and How to Avoid Them in Factors of 1694
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 as 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 1694, 1 and 1694 are also factors.
Factors of 1694 Examples
Problem 1
There are 1694 chairs to be arranged in an auditorium. If each row can have a maximum of 2 chairs, how many rows will there be?
There will be 847 rows.
Explanation
To find the number of rows, divide the total chairs by the number of chairs per row.
1694/2 = 847
Problem 2
A company has 1694 employees and wants to form teams with 13 people each. How many teams can they form?
They can form 130 teams.
Explanation
To find the number of teams, divide the total employees by the number of people per team.
1694/13 = 130
Problem 3
A farmer has 1694 apples to pack in 29 boxes. How many apples will each box contain?
Each box will contain 58 apples.
Explanation
To find the number of apples per box, divide the total apples by the number of boxes.
1694/29 = 58
Problem 4
A publisher printed 1694 copies of a book and plans to distribute them equally among 169 stores. How many copies will each store receive?
Each store will receive 10 copies.
Explanation
Dividing the copies by the number of stores, we will find the number of copies per store.
1694/169 = 10
Problem 5
A school has 1694 markers to distribute among 6 classrooms. How many markers will each classroom receive?
Each classroom will receive 282 markers, with 2 markers remaining.
Explanation
Divide the total markers by the number of classrooms.
1694/6 = 282 remainder 2
FAQs on Factors of 1694
1.What are the factors of 1694?
2.Mention the prime factors of 1694.
3.Is 1694 a multiple of 29?
4.Mention the factor pairs of 1694?
5.What is the square of 1694?
Important Glossaries for Factors of 1694
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1694 are 1, 2, 13, 26, 29, 58, 169, 338, 847, and 1694.
- Prime factors: The factors which are prime numbers. For example, 2 and 169 are prime factors of 1694.
- 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 1694 are (1, 1694), (2, 847).
- Prime factorization: Breaking down a number into its basic prime number components. For example, the prime factorization of 1694 is 2 × 3 × 169.
- Multiplication method: A method to find factors by identifying number pairs that multiply to the original number.
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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.
