118 LearnersLast updated on May 26th, 2025
Factors of 1629
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 1629, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1629?
The numbers that divide 1629 evenly are known as factors of 1629.
A factor of 1629 is a number that divides the number without remainder.
The factors of 1629 are 1, 3, 9, 181, 543, and 1629.
Negative factors of 1629: -1, -3, -9, -181, -543, and -1629.
Prime factors of 1629: 3 and 181.
Prime factorization of 1629: 3² × 181.
The sum of factors of 1629: 1 + 3 + 9 + 181 + 543 + 1629 = 2366
How to Find Factors of 1629?
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 1629. Identifying the numbers which are multiplied to get the number 1629 is the multiplication method.
Step 1: Multiply 1629 by 1, 1629 × 1 = 1629.
Step 2: Check for other numbers that give 1629 after multiplying
3 × 543 = 1629
9 × 181 = 1629
Therefore, the positive factor pairs of 1629 are: (1, 1629), (3, 543), (9, 181). All these factor pairs result in 1629.
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 a simple division method
Step 1: Divide 1629 by 1, 1629 ÷ 1 = 1629.
Step 2: Continue dividing 1629 by the numbers until the remainder becomes 0.
1629 ÷ 1 = 1629
1629 ÷ 3 = 543
1629 ÷ 9 = 181
Therefore, the factors of 1629 are: 1, 3, 9, 181, 543, 1629.
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 1629 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1629 ÷ 3 = 543
543 ÷ 3 = 181
181 ÷ 181 = 1
The prime factors of 1629 are 3 and 181.
The prime factorization of 1629 is: 3² × 181.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1629 is divided by 3 to get 543.
Step 2: Now divide 543 by 3 to get 181. Here, 181 is a prime number and cannot be divided further. So, the prime factorization of 1629 is: 3² × 181.
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 1629: (1, 1629), (3, 543), (9, 181).
Negative factor pairs of 1629: (-1, -1629), (-3, -543), (-9, -181).
Common Mistakes and How to Avoid Them in Factors of 1629
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 1629, 1 and 1629 is also a factor.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1629 consist of -1, -3, -9, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1629/1.5 = 1086, 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 1629 are prime numbers. For example, 3 and 181 are the prime factors of 1629, but it has other factors like 9, 543.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1629 as 3² × 181 and missing all the key factors.
Factors of 1629 Examples
Problem 1
There are 3 teams and 1629 points. How will they distribute the points equally?
They will get 543 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
1629/3 = 543
Problem 2
A rectangular garden has a length of 9 meters and a total area of 1629 square meters. Find the width.
181 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1629 = 9 × width
To find the value of width, we need to shift 9 to the left side.
1629/9 = width
Width = 181.
Problem 3
There are 9 boxes and 1629 marbles. How many marbles will be in each box?
Each box will have 181 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1629/9 = 181
Problem 4
In a class, there are 1629 students, and 9 groups. How many students are there in each group?
There are 181 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1629/9 = 181
Problem 5
1629 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 181 books.
Explanation
Divide total books by shelves.
1629/9 = 181
FAQs on Factors of 1629
1.What are the factors of 1629?
2.Mention the prime factors of 1629.
3.Is 1629 a multiple of 9?
4.Mention the factor pairs of 1629?
5.What is the square of 1629?
Important Glossaries for Factors of 1629
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1629 are 1, 3, 9, 181, 543, and 1629.
- Prime factors: The factors which are prime numbers. For example, 3 and 181 are prime factors of 1629.
- 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 1629 are (1, 1629), (3, 543), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1629 is 3² × 181.
- Multiple: A number that can be divided by another number without a remainder. For example, 1629 is a multiple of 9.
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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.
