121 LearnersLast updated on May 26th, 2025
Factors of 3150
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 3150, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 3150?
The numbers that divide 3150 evenly are known as factors of 3150.
A factor of 3150 is a number that divides the number without remainder.
The factors of 3150 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150.
Negative factors of 3150: -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -25, -30, -35, -42, -45, -50, -63, -70, -75, -90, -105, -126, -150, -175, -210, -225, -315, -350, -450, -525, -630, -1050, -1575, and -3150.
Prime factors of 3150: 2, 3, 5, and 7.
Prime factorization of 3150: 2 × 3² × 5² × 7.
The sum of factors of 3150: 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 25 + 30 + 35 + 42 + 45 + 50 + 63 + 70 + 75 + 90 + 105 + 126 + 150 + 175 + 210 + 225 + 315 + 350 + 450 + 525 + 630 + 1050 + 1575 + 3150 = 9360.
How to Find Factors of 3150?
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 3150. Identifying the numbers which are multiplied to get the number 3150 is the multiplication method.
Step 1: Multiply 3150 by 1, 3150 × 1 = 3150.
Step 2: Check for other numbers that give 3150 after multiplying
2 × 1575 = 3150
3 × 1050 = 3150
5 × 630 = 3150
6 × 525 = 3150
7 × 450 = 3150
9 × 350 = 3150
10 × 315 = 3150
14 × 225 = 3150
15 × 210 = 3150
18 × 175 = 3150
21 × 150 = 3150
25 × 126 = 3150
30 × 105 = 3150
35 × 90 = 3150
42 × 75 = 3150
45 × 70 = 3150
50 × 63 = 3150
Therefore, the positive factor pairs of 3150 are: (1, 3150), (2, 1575), (3, 1050), (5, 630), (6, 525), (7, 450), (9, 350), (10, 315), (14, 225), (15, 210), (18, 175), (21, 150), (25, 126), (30, 105), (35, 90), (42, 75), (45, 70), (50, 63). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with 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 3150 by 1, 3150 ÷ 1 = 3150.
Step 2: Continue dividing 3150 by the numbers until the remainder becomes 0.
3150 ÷ 1 = 3150
3150 ÷ 2 = 1575
3150 ÷ 3 = 1050
3150 ÷ 5 = 630
3150 ÷ 6 = 525
3150 ÷ 7 = 450
3150 ÷ 9 = 350
3150 ÷ 10 = 315
3150 ÷ 14 = 225
3150 ÷ 15 = 210
3150 ÷ 18 = 175
3150 ÷ 21 = 150
3150 ÷ 25 = 126
3150 ÷ 30 = 105
3150 ÷ 35 = 90
3150 ÷ 42 = 75
3150 ÷ 45 = 70
3150 ÷ 50 = 63
Therefore, the factors of 3150 are: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150.
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 3150 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3150 ÷ 2 = 1575
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
The prime factors of 3150 are 2, 3, 5, and 7.
The prime factorization of 3150 is: 2 × 3² × 5² × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 3150 is divided by 2 to get 1575.
Step 2: Now divide 1575 by 3 to get 525.
Step 3: Then divide 525 by 3 to get 175.
Step 4: Divide 175 by 5 to get 35.
Step 5: Divide 35 by 5 to get 7. Here, 7 is a prime number, and it cannot be divided anymore. So, the prime factorization of 3150 is: 2 × 3² × 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 3150: (1, 3150), (2, 1575), (3, 1050), (5, 630), (6, 525), (7, 450), (9, 350), (10, 315), (14, 225), (15, 210), (18, 175), (21, 150), (25, 126), (30, 105), (35, 90), (42, 75), (45, 70), (50, 63).
Negative factor pairs of 3150: (-1, -3150), (-2, -1575), (-3, -1050), (-5, -630), (-6, -525), (-7, -450), (-9, -350), (-10, -315), (-14, -225), (-15, -210), (-18, -175), (-21, -150), (-25, -126), (-30, -105), (-35, -90), (-42, -75), (-45, -70), (-50, -63).
Common Mistakes and How to Avoid Them in Factors of 3150
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 word. Always remember to include 1 and the number itself.
For example, in the factors of 3150, 1 and 3150 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 3150 consist of -1, -2, -3, 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 3150/1.5 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 3150 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of 3150, but it has other factors like 9, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3150 as 2 × 3² × 5² × 7 and missing all the key factors.
Factors of 3150 Examples
Problem 1
There are 3150 apples and 7 baskets. How will they divide it equally?
They will get 450 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
3150/7 = 450
Problem 2
A rectangular plot has a width of 30 meters and a total area of 3150 square meters. Find the length?
105 meters.
Explanation
To find the length of the plot, we use the formula,
Area = length × width
3150 = length × 30
To find the value of the length, we need to shift 30 to the left side.
3150/30 = length
Length = 105.
Problem 3
There are 9 trays and 3150 eggs. How many eggs will be in each tray?
Each tray will have 350 eggs.
Explanation
To find the eggs in each tray, divide the total eggs by the trays.
3150/9 = 350
Problem 4
A school has 3150 students, and they want to form 25 groups. How many students are there in each group?
There are 126 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
3150/25 = 126
Problem 5
3150 pages need to be printed in 21 booklets. How many pages will go in each booklet?
Each of the booklets has 150 pages.
Explanation
Divide total pages by booklets.
3150/21 = 150
FAQs on Factors of 3150
1.What are the factors of 3150?
2.Mention the prime factors of 3150.
3.Is 3150 a multiple of 9?
4.Mention the factor pairs of 3150?
5.What is the square of 3150?
6.How can children in Qatar use numbers in everyday life to understand Factors of 3150?
7.What are some fun ways kids in Qatar can practice Factors of 3150 with numbers?
8.What role do numbers and Factors of 3150 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 3150 skills?
Important Glossaries for Factors of 3150
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3150 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, and 3150.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 3150.
- 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 3150 are (1, 3150), (2, 1575), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 3150 is 2 × 3² × 5² × 7.
- Multiple: A number that can be divided by another number without a remainder. For example, 3150 is a multiple of 9.
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About BrightChamps in Qatar
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.
