118 LearnersLast updated on May 26th, 2025
Factors of 1631
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 1631, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1631?
The numbers that divide 1631 evenly are known as factors of 1631.
A factor of 1631 is a number that divides the number without remainder.
The factors of 1631 are 1, 19, 61, 323, 1631.
Negative factors of 1631: -1, -19, -61, -323, -1631.
Prime factors of 1631: 19 and 61.
Prime factorization of 1631: 19 × 61.
The sum of factors of 1631: 1 + 19 + 61 + 323 + 1631 = 2035
How to Find Factors of 1631?
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 1631. Identifying the numbers which are multiplied to get the number 1631 is the multiplication method.
Step 1: Multiply 1631 by 1, 1631 × 1 = 1631.
Step 2: Check for other numbers that give 1631 after multiplying 19 × 61 = 1631 Therefore, the positive factor pairs of 1631 are: (1, 1631), (19, 61). All these factor pairs result in 1631.
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 1631 by 1, 1631 ÷ 1 = 1631.
Step 2: Continue dividing 1631 by the numbers until the remainder becomes 0.
1631 ÷ 1 = 1631
1631 ÷ 19 = 61
Therefore, the factors of 1631 are: 1, 19, 61, 323, 1631.
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 1631 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1631 ÷ 19 = 61
61 ÷ 61 = 1
The prime factors of 1631 are 19 and 61.
The prime factorization of 1631 is: 19 × 61.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1631 is divided by 19 to get 61.
Step 2: Now divide 61 by 61 to get 1. Here, 61 is a prime number, that cannot be divided anymore. So, the prime factorization of 1631 is: 19 × 61.
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 1631: (1, 1631), (19, 61).
Negative factor pairs of 1631: (-1, -1631), (-19, -61).
Common Mistakes and How to Avoid Them in Factors of 1631
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 1631, 1 and 1631 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 1631 consist of -1, -19, -61, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1631/1.5 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 1631 are prime numbers. For example, 19 and 61 are the prime factors of 1631, but it has other factors like 323.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1631 as 19 × 61 and missing all the key factors.
Factors of 1631 Examples
Problem 1
There are 19 teams and 1631 participants. How will they divide the participants equally among the teams?
They will have 61 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1631 ÷ 19 = 61
Problem 2
A road is 323 meters long, and workers are placing poles every 19 meters. How many poles will be placed?
17 poles.
Explanation
To find the number of poles, divide the total length by the distance between each pole.
323 ÷ 19 = 17
Problem 3
There are 61 boxes and 1631 items. How many items will be in each box?
Each box will have 27 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
1631 ÷ 61 = 27
Problem 4
In a stadium, there are 1631 seats, and 5 sections. How many seats are there in each section?
There are 326 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
1631 ÷ 5 = 326
Problem 5
1631 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 233 books.
Explanation
Divide total books by shelves.
1631 ÷ 7 = 233
FAQs on Factors of 1631
1.What are the factors of 1631?
2.Mention the prime factors of 1631.
3.Is 1631 a multiple of 19?
4.Mention the factor pairs of 1631?
5.What is the square of 1631?
Important Glossaries for Factors of 1631
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1631 are 1, 19, 61, 323, and 1631.
- Prime factors: The factors which are prime numbers. For example, 19 and 61 are prime factors of 1631.
- 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 1631 are (1, 1631), (19, 61).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1631 is 19 × 61.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1631 is a multiple of 19.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 1631
![Important Math Links Icon]()
Next to Factors of 1631
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.
