103 LearnersLast updated on May 26th, 2025
Factors of 10500
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 10500, how they are used in real life, and tips to learn them quickly.
What are the Factors of 10500?
The numbers that divide 10500 evenly are known as factors of 10500.
A factor of 10500 is a number that divides the number without remainder.
The factors of 10500 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 750, 1050, 1400, 1500, 2100, 2625, 3500, 5250, and 10500.
Negative factors of 10500: -1, -2, -3, -4, -5, -6, -7, -10, -12, -14, -15, -20, -21, -25, -28, -30, -35, -42, -50, -60, -70, -75, -84, -100, -105, -140, -150, -175, -210, -300, -350, -420, -525, -700, -750, -1050, -1400, -1500, -2100, -2625, -3500, -5250, and -10500.
Prime factors of 10500: 2, 3, 5, and 7.
Prime factorization of 10500: 2² × 3 × 5³ × 7.
The sum of factors of 10500: The sum of all factors of 10500 is 39240.
How to Find Factors of 10500?
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 10500. Identifying the numbers which are multiplied to get the number 10500 is the multiplication method.
Step 1: Multiply 10500 by 1, 10500 × 1 = 10500.
Step 2: Check for other numbers that give 10500 after multiplying
2 × 5250 = 10500
3 × 3500 = 10500
4 × 2625 = 10500
5 × 2100 = 10500
6 × 1750 = 10500
7 × 1500 = 10500
10 × 1050 = 10500
12 × 875 = 10500
14 × 750 = 10500
15 × 700 = 10500
20 × 525 = 10500
21 × 500 = 10500
25 × 420 = 10500
28 × 375 = 10500
30 × 350 = 10500
35 × 300 = 10500
42 × 250 = 10500
50 × 210 = 10500
60 × 175 = 10500
70 × 150 = 10500
75 × 140 = 10500
84 × 125 = 10500
100 × 105 = 10500
105 × 100 = 10500
140 × 75 = 10500
150 × 70 = 10500
175 × 60 = 10500
210 × 50 = 10500
300 × 35 = 10500
350 × 30 = 10500
420 × 25 = 10500
525 × 20 = 10500
700 × 15 = 10500
750 × 14 = 10500
875 × 12 = 10500
1050 × 10 = 10500
1500 × 7 = 10500
1750 × 6 = 10500
2100 × 5 = 10500
2625 × 4 = 10500
3500 × 3 = 10500
5250 × 2 = 10500
Therefore, the positive factor pairs of 10500 are: (1, 10500), (2, 5250), (3, 3500), (4, 2625), (5, 2100), (6, 1750), (7, 1500), (10, 1050), (12, 875), (14, 750), (15, 700), (20, 525), (21, 500), (25, 420), (28, 375), (30, 350), (35, 300), (42, 250), (50, 210), (60, 175), (70, 150), (75, 140), (84, 125), (100, 105).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 the simple division method:
Step 1: Divide 10500 by 1, 10500 ÷ 1 = 10500.
Step 2: Continue dividing 10500 by the numbers until the remainder becomes 0.
10500 ÷ 1 = 10500
10500 ÷ 2 = 5250
10500 ÷ 3 = 3500
10500 ÷ 4 = 2625
10500 ÷ 5 = 2100
10500 ÷ 6 = 1750
10500 ÷ 7 = 1500
10500 ÷ 10 = 1050
10500 ÷ 12 = 875
10500 ÷ 14 = 750
10500 ÷ 15 = 700
10500 ÷ 20 = 525
10500 ÷ 21 = 500
10500 ÷ 25 = 420
10500 ÷ 28 = 375
10500 ÷ 30 = 350
10500 ÷ 35 = 300
10500 ÷ 42 = 250
10500 ÷ 50 = 210
10500 ÷ 60 = 175
10500 ÷ 70 = 150
10500 ÷ 75 = 140
10500 ÷ 84 = 125
10500 ÷ 100 = 105
Therefore, the factors of 10500 are: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 750, 1050, 1400, 1500, 2100, 2625, 3500, 5250, and 10500.
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 10500 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
10500 ÷ 2 = 5250
5250 ÷ 2 = 2625
2625 ÷ 3 = 875
875 ÷ 5 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
The prime factors of 10500 are 2, 3, 5, and 7.
The prime factorization of 10500 is: 2² × 3 × 5³ × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows how to construct a factor tree for 10500:
Step 1: Firstly, 10500 is divided by 2 to get 5250.
Step 2: Now divide 5250 by 2 to get 2625.
Step 3: Then divide 2625 by 3 to get 875.
Step 4: Divide 875 by 5 to get 175
Step 5: Divide 175 by 5 to get 35.
Step 6: Divide 35 by 5 to get 7.
Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 10500 is: 2² × 3 × 5³ × 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 10500: (1, 10500), (2, 5250), (3, 3500), (4, 2625), (5, 2100), (6, 1750), (7, 1500), (10, 1050), (12, 875), (14, 750), (15, 700), (20, 525), (21, 500), (25, 420), (28, 375), (30, 350), (35, 300), (42, 250), (50, 210), (60, 175), (70, 150), (75, 140), (84, 125), (100, 105).
Negative factor pairs of 10500: (-1, -10500), (-2, -5250), (-3, -3500), (-4, -2625), (-5, -2100), (-6, -1750), (-7, -1500), (-10, -1050), (-12, -875), (-14, -750), (-15, -700), (-20, -525), (-21, -500), (-25, -420), (-28, -375), (-30, -350), (-35, -300), (-42, -250), (-50, -210), (-60, -175), (-70, -150), (-75, -140), (-84, -125), (-100, -105).
Common Mistakes and How to Avoid Them in Factors of 10500
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 10500, 1 and 10500 are also factors.
Factors of 10500 Examples
Problem 1
A scientist has 10500 samples of a chemical solution. She wants to distribute them equally into containers, each holding 250 samples. How many containers will she need?
She will need 42 containers.
Explanation
To divide the samples equally, we need to divide the total samples by the capacity of each container.
10500/250 = 42
Problem 2
A factory produces 10500 widgets every hour. If they are packed into boxes of 35 widgets each, how many boxes are needed for one hour of production?
300 boxes.
Explanation
To find the number of boxes needed, divide the total widgets by the widgets per box.
10500/35 = 300
Problem 3
A concert hall has a seating capacity of 10500 seats. If the seats are arranged in 21 equal rows, how many seats are there in each row?
Each row will have 500 seats.
Explanation
To find the seats in each row, divide the total seats by the number of rows.
10500/21 = 500
Problem 4
A bakery makes 10500 loaves of bread. If they are packed into bundles of 5 loaves each, how many bundles will be made?
2100 bundles.
Explanation
Dividing the total loaves by the loaves per bundle, we get the number of bundles.
10500/5 = 2100
Problem 5
A farm has 10500 apples that need to be packed into baskets, each containing 70 apples. How many baskets are required?
150 baskets.
Explanation
Divide the total number of apples by the number of apples per basket to determine the number of baskets needed.
10500/70 = 150
FAQs on Factors of 10500
1.What are the factors of 10500?
2.Mention the prime factors of 10500.
3.Is 10500 a multiple of 7?
4.Mention the factor pairs of 10500?
5.What is the square of 10500?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 10500?
7.What are some fun ways kids in United Kingdom can practice Factors of 10500 with numbers?
8.What role do numbers and Factors of 10500 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 10500 skills?
Important Glossaries for Factor of 10500
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 10500 are 1, 2, 3, 4, 5, 6, 7, 10, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 10500.
- 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 10500 are (1, 10500), (2, 5250), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 10500 is 2² × 3 × 5³ × 7.
- Multiple: A number that can be divided by another number without a remainder. For example, 10500 is a multiple of 7.
Explore More numbers
Previous to Factors of 10500
About BrightChamps in United Kingdom
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.
