101 LearnersLast updated on May 26th, 2025
Factors of 1050
Factors are the numbers that divide any given number evenly without a 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 1050, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1050?
The numbers that divide 1050 evenly are known as factors of 1050.
A factor of 1050 is a number that divides the number without a remainder.
The factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050.
Negative factors of 1050: -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -25, -30, -35, -42, -50, -70, -75, -105, -150, -175, -210, -350, -525, and -1050.
Prime factors of 1050: 2, 3, 5, and 7.
Prime factorization of 1050: 2 × 3 × 5² × 7.
The sum of factors of 1050 is: 1 + 2 + 3 + 5 + 6 + 7 + 10 + 14 + 15 + 21 + 25 + 30 + 35 + 42 + 50 + 70 + 75 + 105 + 150 + 175 + 210 + 350 + 525 + 1050 = 3724
How to Find Factors of 1050?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1050. Identifying the numbers which are multiplied to get the number 1050 is the multiplication method.
Step 1: Multiply 1050 by 1, 1050 × 1 = 1050.
Step 2: Check for other numbers that give 1050 after multiplying
2 × 525 = 1050
3 × 350 = 1050
5 × 210 = 1050
6 × 175 = 1050
7 × 150 = 1050
10 × 105 = 1050
14 × 75 = 1050
15 × 70 = 1050
21 × 50 = 1050
25 × 42 = 1050
30 × 35 = 1050
Therefore, the positive factor pairs of 1050 are: (1, 1050), (2, 525), (3, 350), (5, 210), (6, 175), (7, 150), (10, 105), (14, 75), (15, 70), (21, 50), (25, 42), (30, 35). 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 1050 by 1, 1050 ÷ 1 = 1050.
Step 2: Continue dividing 1050 by the numbers until the remainder becomes 0.
1050 ÷ 1 = 1050
1050 ÷ 2 = 525
1050 ÷ 3 = 350
1050 ÷ 5 = 210
1050 ÷ 6 = 175
1050 ÷ 7 = 150
1050 ÷ 10 = 105
1050 ÷ 14 = 75
1050 ÷ 15 = 70
1050 ÷ 21 = 50
1050 ÷ 25 = 42
1050 ÷ 30 = 35
Therefore, the factors of 1050 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1050 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1050 ÷ 2 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 1050 are 2, 3, 5, and 7.
The prime factorization of 1050 is: 2 × 3 × 5² × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1050 is divided by 2 to get 525.
Step 2: Now divide 525 by 3 to get 175.
Step 3: Then divide 175 by 5 to get 35.
Step 4: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1050 is: 2 × 3 × 5² × 7.
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 1050: (1, 1050), (2, 525), (3, 350), (5, 210), (6, 175), (7, 150), (10, 105), (14, 75), (15, 70), (21, 50), (25, 42), (30, 35).
Negative factor pairs of 1050: (-1, -1050), (-2, -525), (-3, -350), (-5, -210), (-6, -175), (-7, -150), (-10, -105), (-14, -75), (-15, -70), (-21, -50), (-25, -42), (-30, -35).
Common Mistakes and How to Avoid Them in Factors of 1050
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 1050, 1 and 1050 are also factors.
Factors of 1050 Examples
Problem 1
There are 15 friends and 1050 marbles. How will they divide it equally?
They will get 70 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
1050/15 = 70
Problem 2
A rectangular field has a length of 25 meters and a total area of 1050 square meters. Find the width.
42 meters.
Explanation
To find the width of the field, we use the formula:
Area = length × width
1050 = 25 × width
To find the value of width, we need to shift 25 to the left side.
1050/25 = width
Width = 42.
Problem 3
There are 35 boxes and 1050 candies. How many candies will be in each box?
Each box will have 30 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
1050/35 = 30
Problem 4
In a class, there are 1050 students, and 50 groups. How many students are there in each group?
There are 21 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1050/50 = 21
Problem 5
1050 books need to be arranged on 7 shelves. How many books will go on each shelf?
Each of the shelves has 150 books.
Explanation
Divide total books by shelves.
1050/7 = 150
FAQs on Factors of 1050
1.What are the factors of 1050?
2.Mention the prime factors of 1050.
3.Is 1050 a multiple of 5?
4.Mention the factor pairs of 1050?
5.What is the square of 1050?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1050?
7.What are some fun ways kids in Bahrain can practice Factors of 1050 with numbers?
8.What role do numbers and Factors of 1050 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1050 skills?
Important Glossaries for Factors of 1050
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 1050.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1050 is 2 × 3 × 5² × 7.
- 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 1050 are (1, 1050), (2, 525), etc.
- Multiplication method: A method to find factors by identifying number pairs that multiply to the given number. For example, using the multiplication method for 1050 gives pairs like (3, 350) and (5, 210).
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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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