100 LearnersLast updated on May 26th, 2025
Factors of 1674
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 1674, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1674?
The numbers that divide 1674 evenly are known as factors of 1674. A factor of 1674 is a number that divides the number without remainder.
The factors of 1674 are 1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837, and 1674.
Negative factors of 1674: -1, -2, -3, -6, -9, -18, -27, -31, -54, -62, -93, -186, -279, -558, -837, and -1674.
Prime factors of 1674: 2, 3, and 31.
Prime factorization of 1674: 2 × 33 × 31.
The sum of factors of 1674: 1 + 2 + 3 + 6 + 9 + 18 + 27 + 31 + 54 + 62 + 93 + 186 + 279 + 558 + 837 + 1674 = 3842
How to Find Factors of 1674?
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 1674. Identifying the numbers which are multiplied to get the number 1674 is the multiplication method.
Step 1: Multiply 1674 by 1, 1674 × 1 = 1674.
Step 2: Check for other numbers that give 1674 after multiplying
2 × 837 = 1674
3 × 558 = 1674
6 × 279 = 1674
9 × 186 = 1674
18 × 93 = 1674
27 × 62 = 1674
31 × 54 = 1674
Therefore, the positive factor pairs of 1674 are: (1, 1674), (2, 837), (3, 558), (6, 279), (9, 186), (18, 93), (27, 62), (31, 54). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1674 by 1, 1674 ÷ 1 = 1674.
Step 2: Continue dividing 1674 by the numbers until the remainder becomes 0.
1674 ÷ 1 = 1674
1674 ÷ 2 = 837
1674 ÷ 3 = 558
1674 ÷ 6 = 279
1674 ÷ 9 = 186
1674 ÷ 18 = 93
1674 ÷ 27 = 62
1674 ÷ 31 = 54
Therefore, the factors of 1674 are: 1, 2, 3, 6, 9, 18, 27, 31, 54, 62, 93, 186, 279, 558, 837, 1674.
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 1674 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1674 ÷ 2 = 837
837 ÷ 3 = 279
279 ÷ 3 = 93
93 ÷ 3 = 31
31 ÷ 31 = 1
The prime factors of 1674 are 2, 3, and 31.
The prime factorization of 1674 is: 2 × 33 × 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, 1674 is divided by 2 to get 837.
Step 2: Now divide 837 by 3 to get 279.
Step 3: Then divide 279 by 3 to get 93.
Step 4: Divide 93 by 3 to get 31. Here, 31 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1674 is: 2 × 33 × 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 1674: (1, 1674), (2, 837), (3, 558), (6, 279), (9, 186), (18, 93), (27, 62), (31, 54).
Negative factor pairs of 1674: (-1, -1674), (-2, -837), (-3, -558), (-6, -279), (-9, -186), (-18, -93), (-27, -62), (-31, -54).
Common Mistakes and How to Avoid Them in Factors of 1674
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 1674, 1 and 1674 are also factors.
Factors of 1674 Examples
Problem 1
There are 18 students and 1674 pencils. How will they divide them equally?
They will get 93 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
1674/18 = 93
Problem 2
A rectangular garden has a length of 54 meters and a total area of 1674 square meters. Find the width.
31 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1674 = 54 × width
To find the value of width, we need to shift 54 to the left side.
1674/54 = width
Width = 31.
Problem 3
There are 6 baskets and 1674 fruits. How many fruits will be in each basket?
Each basket will have 279 fruits.
Explanation
To find the fruits in each basket, divide the total fruits by the baskets.
1674/6 = 279
Problem 4
In a conference, there are 93 attendees and 9 tables. How many attendees are there at each table?
There are 10 attendees at each table.
Explanation
Dividing the attendees by the total tables, we will get the number of attendees at each table.
93/9 = 10
Problem 5
1674 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 54 books.
Explanation
Divide total books by shelves.
1674/31 = 54
FAQs on Factors of 1674
1.What are the factors of 1674?
2.Mention the prime factors of 1674.
3.Is 1674 a multiple of 27?
4.Mention the factor pairs of 1674?
5.What is the square of 1674?
Important Glossaries for Factors of 1674
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1674 are 1, 2, 3, 6, 9, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 31 are prime factors of 1674.
- 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 1674 are (1, 1674), (2, 837), etc.
- Multiplication Method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, 2 × 837 = 1674.
- Division Method: A method to find factors by dividing the original number by potential factors until the division is exact. For example, 1674 ÷ 3 = 558.
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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.
