123 LearnersLast updated on May 26th, 2025
Factors of 1630
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 1630, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1630?
The numbers that divide 1630 evenly are known as factors of 1630.
A factor of 1630 is a number that divides the number without remainder.
The factors of 1630 are 1, 2, 5, 10, 163, 326, 815, and 1630.
Negative factors of 1630: -1, -2, -5, -10, -163, -326, -815, and -1630.
Prime factors of 1630: 2, 5, and 163.
Prime factorization of 1630: 2 × 5 × 163.
The sum of factors of 1630: 1 + 2 + 5 + 10 + 163 + 326 + 815 + 1630 = 2952
How to Find Factors of 1630?
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 1630. Identifying the numbers which are multiplied to get the number 1630 is the multiplication method.
Step 1: Multiply 1630 by 1, 1630 × 1 = 1630.
Step 2: Check for other numbers that give 1630 after multiplying
2 × 815 = 1630
5 × 326 = 1630
10 × 163 = 1630
Therefore, the positive factor pairs of 1630 are: (1, 1630), (2, 815), (5, 326), (10, 163). All these factor pairs result in 1630.
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 1630 by 1, 1630 ÷ 1 = 1630.
Step 2: Continue dividing 1630 by the numbers until the remainder becomes 0.
1630 ÷ 1 = 1630
1630 ÷ 2 = 815
1630 ÷ 5 = 326
1630 ÷ 10 = 163
Therefore, the factors of 1630 are: 1, 2, 5, 10, 163, 326, 815, 1630.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 1630 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1630 ÷ 2 = 815
815 ÷ 5 = 163
163 ÷ 163 = 1
The prime factors of 1630 are 2, 5, and 163.
The prime factorization of 1630 is: 2 × 5 × 163.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1630 is divided by 2 to get 815.
Step 2: Now divide 815 by 5 to get 163.
Step 3: 163 is a prime number, which cannot be divided further. So, the prime factorization of 1630 is: 2 × 5 × 163.
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 1630: (1, 1630), (2, 815), (5, 326), and (10, 163).
Negative factor pairs of 1630: (-1, -1630), (-2, -815), (-5, -326), and (-10, -163).
Common Mistakes and How to Avoid Them in Factors of 1630
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 1630, 1 and 1630 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1630 consist of -1, -2, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1630/1.5 = 1086.666, 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 1630 are prime numbers. While 2, 5, and 163 are the prime factors of 1630, it has other factors like 10, 326.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1630 as 2 × 5 × 163 and missing all the key factors.
Factors of 1630 Examples
Problem 1
There are 10 teams and 1630 participants. How will they divide it equally?
Each team will have 163 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1630/10 = 163
Problem 2
A rectangular garden is 5 meters wide, and the total area is 1630 square meters. Find the length?
326 meters.
Explanation
To find the length of the garden, we use the formula, Area = length × width
1630 = 5 × length
To find the value of length, we need to shift 5 to the left side.
1630/5 = length
Length = 326.
Problem 3
There are 163 bags and 1630 marbles. How many marbles will be in each bag?
Each bag will have 10 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the number of bags.
1630/163 = 10
Problem 4
In a class, there are 815 students, and 5 groups. How many students are there in each group?
There are 163 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
815/5 = 163
Problem 5
1630 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each shelf will have 815 books.
Explanation
Divide total books by shelves.
1630/2 = 815
FAQs on Factors of 1630
1.What are the factors of 1630?
2.Mention the prime factors of 1630.
3.Is 1630 a multiple of 5?
4.Mention the factor pairs of 1630?
5.What is the square of 1630?
Important Glossaries for Factor of 1630
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1630 are 1, 2, 5, 10, 163, 326, 815, and 1630.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 163 are prime factors of 1630.
- 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 1630 are (1, 1630), (2, 815), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1630 is 2 × 5 × 163.
- Multiplication method: A method to find factors by identifying pairs of numbers that give a product equal to the original number. For example, 2 × 815 = 1630.
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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.
