120 LearnersLast updated on May 26th, 2025
Factors of 1692
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 1692, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1692?
The numbers that divide 1692 evenly are known as factors of 1692.
A factor of 1692 is a number that divides the number without remainder.
The factors of 1692 are 1, 2, 3, 4, 6, 12, 141, 282, 423, 564, 846, and 1692.
Negative factors of 1692: -1, -2, -3, -4, -6, -12, -141, -282, -423, -564, -846, and -1692.
Prime factors of 1692: 2, 3, and 47.
Prime factorization of 1692: 22 × 3 × 47.
The sum of factors of 1692: 1 + 2 + 3 + 4 + 6 + 12 + 141 + 282 + 423 + 564 + 846 + 1692 = 3976
How to Find Factors of 1692?
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 1692. Identifying the numbers which are multiplied to get the number 1692 is the multiplication method.
Step 1: Multiply 1692 by 1, 1692 × 1 = 1692.
Step 2: Check for other numbers that give 1692 after multiplying
2 × 846 = 1692
3 × 564 = 1692
4 × 423 = 1692
6 × 282 = 1692
12 × 141 = 1692
Therefore, the positive factor pairs of 1692 are: (1, 1692), (2, 846), (3, 564), (4, 423), (6, 282), (12, 141).
All these factor pairs result in 1692.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 1692 by 1, 1692 ÷ 1 = 1692.
Step 2: Continue dividing 1692 by the numbers until the remainder becomes 0.
1692 ÷ 1 = 1692
1692 ÷ 2 = 846
1692 ÷ 3 = 564
1692 ÷ 4 = 423
1692 ÷ 6 = 282
1692 ÷ 12 = 141
Therefore, the factors of 1692 are: 1, 2, 3, 4, 6, 12, 141, 282, 423, 564, 846, 1692.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1692 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1692 ÷ 2 = 846
846 ÷ 2 = 423
423 ÷ 3 = 141
141 ÷ 3 = 47
47 ÷ 47 = 1
The prime factors of 1692 are 2, 3, and 47.
The prime factorization of 1692 is: 22 × 3 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1692 is divided by 2 to get 846.
Step 2: Now divide 846 by 2 to get 423.
Step 3: Then divide 423 by 3 to get 141.
Step 4: Divide 141 by 3 to get 47. Here, 47 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1692 is: 22 × 3 × 47.
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 1692: (1, 1692), (2, 846), (3, 564), (4, 423), (6, 282), (12, 141).
Negative factor pairs of 1692: (-1, -1692), (-2, -846), (-3, -564), (-4, -423), (-6, -282), (-12, -141).
Common Mistakes and How to Avoid Them in Factors of 1692
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 1692, 1 and 1692 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 1692 consist of -1, -2, -3, 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 1692/1.5 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 1692 are prime numbers.
For example, 2, 3, and 47 are the prime factors of 1692, but it has other factors like 4, 6.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1692 as 22 × 3 × 47 and missing all the key factors.
Factors of 1692 Examples
Problem 1
There are 6 teams and 1692 participants. How will they divide it equally?
They will get 282 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1692/6 = 282
Problem 2
A field is rectangular, the length of the field is 282 meters and the total area is 1692 square meters. Find the width?
6 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1692 = 282 × width
To find the value of width, we need to shift 282 to the left side.
1692/282 = width
Width = 6.
Problem 3
There are 12 crates and 1692 apples. How many apples will be in each crate?
Each crate will have 141 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
1692/12 = 141
Problem 4
In a class, there are 1692 students, and 141 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1692/141 = 12
Problem 5
1692 books need to be arranged in 47 shelves. How many books will go on each shelf?
Each of the shelves has 36 books.
Explanation
Divide total books by shelves.
1692/47 = 36
FAQs on Factors of 1692
1.What are the factors of 1692?
2.Mention the prime factors of 1692.
3.Is 1692 a multiple of 3?
4.Mention the factor pairs of 1692?
5.What is the square of 1692?
6.How can children in Philippines use numbers in everyday life to understand Factors of 1692?
7.What are some fun ways kids in Philippines can practice Factors of 1692 with numbers?
8.What role do numbers and Factors of 1692 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 1692 skills?
Important Glossaries for Factor of 1692
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1692 are 1, 2, 3, 4, 6, 12, 141, 282, 423, 564, 846, and 1692.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 47 are prime factors of 1692.
- 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 1692 are (1, 1692), (2, 846), etc.
- Prime factorization: Breaking down a number into its prime number components. For example, the prime factorization of 1692 is 22 × 3 × 47.
- Multiplication method: A method used to find factor pairs by identifying numbers that multiply to give the original number. For example, 2 × 846 = 1692.
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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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