103 LearnersLast updated on May 26th, 2025
Factors of 1650
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 1650, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1650?
The numbers that divide 1650 evenly are known as factors of 1650. A factor of 1650 is a number that divides the number without remainder. The factors of 1650 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 150, 165, 275, 330, 550, 825, and 1650. Negative factors of 1650: -1, -2, -3, -5, -6, -10, -11, -15, -22, -25, -30, -33, -50, -55, -66, -75, -110, -150, -165, -275, -330, -550, -825, and -1650. Prime factors of 1650: 2, 3, 5, and 11. Prime factorization of 1650: 2 × 3 × 5^2 × 11. The sum of factors of 1650: 1 + 2 + 3 + 5 + 6 + 10 + 11 + 15 + 22 + 25 + 30 + 33 + 50 + 55 + 66 + 75 + 110 + 150 + 165 + 275 + 330 + 550 + 825 + 1650 = 4968
How to Find Factors of 1650?
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 1650. Identifying the numbers which are multiplied to get the number 1650 is the multiplication method. Step 1: Multiply 1650 by 1, 1650 × 1 = 1650. Step 2: Check for other numbers that give 1650 after multiplying 2 × 825 = 1650 3 × 550 = 1650 5 × 330 = 1650 10 × 165 = 1650 15 × 110 = 1650 22 × 75 = 1650 25 × 66 = 1650 30 × 55 = 1650 33 × 50 = 1650 Therefore, the positive factor pairs of 1650 are: (1, 1650), (2, 825), (3, 550), (5, 330), (10, 165), (15, 110), (22, 75), (25, 66), (30, 55), and (33, 50). 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 1650 by 1, 1650 ÷ 1 = 1650. Step 2: Continue dividing 1650 by the numbers until the remainder becomes 0. 1650 ÷ 1 = 1650 1650 ÷ 2 = 825 1650 ÷ 3 = 550 1650 ÷ 5 = 330 1650 ÷ 10 = 165 1650 ÷ 15 = 110 1650 ÷ 22 = 75 1650 ÷ 25 = 66 1650 ÷ 30 = 55 1650 ÷ 33 = 50 Therefore, the factors of 1650 are: 1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 150, 165, 275, 330, 550, 825, and 1650.
Prime Factors and Prime Factorization
The factors can be found by dividing it by 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 1650 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1. 1650 ÷ 2 = 825 825 ÷ 3 = 275 275 ÷ 5 = 55 55 ÷ 5 = 11 11 ÷ 11 = 1 The prime factors of 1650 are 2, 3, 5, and 11. The prime factorization of 1650 is: 2 × 3 × 5^2 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows - Step 1: Firstly, 1650 is divided by 2 to get 825. Step 2: Now divide 825 by 3 to get 275. Step 3: Then divide 275 by 5 to get 55. Step 4: Divide 55 by 5 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1650 is: 2 × 3 × 5^2 × 11. 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 1650: (1, 1650), (2, 825), (3, 550), (5, 330), (10, 165), (15, 110), (22, 75), (25, 66), (30, 55), and (33, 50). Negative factor pairs of 1650: (-1, -1650), (-2, -825), (-3, -550), (-5, -330), (-10, -165), (-15, -110), (-22, -75), (-25, -66), (-30, -55), and (-33, -50).
Common Mistakes and How to Avoid Them in Factors of 1650
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 1650, 1 and 1650 are also factors.
Factors of 1650 Examples
Problem 1
There are 33 students and 1650 apples. How will they divide them equally?
They will get 50 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of students. 1650/33 = 50
Problem 2
A poster is rectangular, the length of the poster is 30 inches and the total area is 1650 square inches. Find the width?
55 inches.
Explanation
To find the width of the poster, we use the formula, Area = length × width 1650 = 30 × width To find the value of width, we need to shift 30 to the left side. 1650/30 = width Width = 55.
Problem 3
There are 22 boxes and 1650 chocolates. How many chocolates will be in each box?
Each box will have 75 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates with the boxes. 1650/22 = 75
Problem 4
In a class, there are 1650 students, and 55 groups. How many students are there in each group?
There are 30 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group. 1650/55 = 30
Problem 5
1650 books need to be arranged in 110 shelves. How many books will go on each shelf?
Each of the shelves has 15 books.
Explanation
Divide total books with shelves. 1650/110 = 15
FAQs on Factors of 1650
1.What are the factors of 1650?
2.Mention the prime factors of 1650.
3.Is 1650 a multiple of 5?
4.Mention the factor pairs of 1650?
5.What is the square of 1650?
Important Glossaries for Factors of 1650
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1650 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 150, 165, 275, 330, 550, 825, and 1650. Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 11 are prime factors of 1650. 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 1650 are (1, 1650), (2, 825), etc. Prime factorization: Breaking down a number into the product of prime numbers. For example, the prime factorization of 1650 is 2 × 3 × 5^2 × 11. Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, the multiplication method for 1650 involves pairs like (1, 1650) and (2, 825).
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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.
