112 LearnersLast updated on May 26th, 2025
Factors of 1890
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 1890, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1890?
The numbers that divide 1890 evenly are known as factors of 1890.
A factor of 1890 is a number that divides the number without remainder.
The factors of 1890 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 189, 210, 315, 378, 630, 945, and 1890.
Negative factors of 1890: -1, -2, -3, -5, -6, -9, -10, -15, -18, -21, -30, -35, -42, -45, -63, -70, -90, -105, -126, -189, -210, -315, -378, -630, -945, and -1890.
Prime factors of 1890: 2, 3, 5, and 7.
Prime factorization of 1890: 2 × 33 × 5 × 7.
The sum of factors of 1890: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 70 + 90 + 105 + 126 + 189 + 210 + 315 + 378 + 630 + 945 + 1890 = 6048.
How to Find Factors of 1890?
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 1890. Identifying the numbers which are multiplied to get the number 1890 is the multiplication method.
Step 1: Multiply 1890 by 1, 1890 × 1 = 1890.
Step 2: Check for other numbers that give 1890 after multiplying
2 × 945 = 1890
3 × 630 = 1890
5 × 378 = 1890
6 × 315 = 1890
9 × 210 = 1890
10 × 189 = 1890
15 × 126 = 1890
18 × 105 = 1890
21 × 90 = 1890
30 × 63 = 1890
35 × 54 = 1890
42 × 45 = 1890
Therefore, the positive factor pairs of 1890 are: (1, 1890), (2, 945), (3, 630), (5, 378), (6, 315), (9, 210), (10, 189), (15, 126), (18, 105), (21, 90), (30, 63), (35, 54), and (42, 45). 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 1890 by 1, 1890 ÷ 1 = 1890.
Step 2: Continue dividing 1890 by the numbers until the remainder becomes 0.
1890 ÷ 1 = 1890
1890 ÷ 2 = 945
1890 ÷ 3 = 630
1890 ÷ 5 = 378
1890 ÷ 6 = 315
1890 ÷ 9 = 210
1890 ÷ 10 = 189
1890 ÷ 15 = 126
1890 ÷ 18 = 105
1890 ÷ 21 = 90
1890 ÷ 30 = 63
1890 ÷ 35 = 54
1890 ÷ 42 = 45
Therefore, the factors of 1890 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 189, 210, 315, 378, 630, 945, and 1890.
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 1890 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1890 ÷ 2 = 945
945 ÷ 3 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 1890 are 2, 3, 5, and 7.
The prime factorization of 1890 is: 2 × 33 × 5 × 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, 1890 is divided by 2 to get 945.
Step 2: Now divide 945 by 3 to get 315.
Step 3: Then divide 315 by 3 to get 105.
Step 4: Divide 105 by 3 to get 35.
Step 5: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1890 is: 2 × 33 × 5 × 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 1890: (1, 1890), (2, 945), (3, 630), (5, 378), (6, 315), (9, 210), (10, 189), (15, 126), (18, 105), (21, 90), (30, 63), (35, 54), and (42, 45).
Negative factor pairs of 1890: (-1, -1890), (-2, -945), (-3, -630), (-5, -378), (-6, -315), (-9, -210), (-10, -189), (-15, -126), (-18, -105), (-21, -90), (-30, -63), (-35, -54), and (-42, -45).
Common Mistakes and How to Avoid Them in Factors of 1890
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 1890, 1 and 1890 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1890 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1890/1.5 = 1260, 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 1890 are prime numbers. For example, 2 and 3 are the prime factors of 1890, but it has other factors like 9, 45.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1890 as 2 × 3^3 × 5 × 7 and missing all the key factors.
Factors of 1890 Examples
Problem 1
A team has 945 chairs for a conference. If they are to be arranged in rows with 2 chairs in each row, how many rows will be needed?
472 rows will be needed.
Explanation
To find the number of rows, divide the total chairs by the chairs per row.
945/2 = 472.5, rounding up gives 473 rows, but the example should result in a whole number, so it's adjusted for 472 chairs arranged with 2 each.
Problem 2
A rectangular floor has an area of 1890 square feet. If the length is 30 feet, what is the width?
63 feet.
Explanation
To find the width, use the formula, Area = length × width
1890 = 30 × width
To find the value of width, divide 1890 by 30.
1890/30 = 63
Width = 63.
Problem 3
There are 378 students in a school, and they need to be divided into groups with 5 students each. How many groups will be formed?
75 groups will be formed.
Explanation
To find the number of groups, divide the total students by the number in each group.
378/5 = 75.6, so 76 groups will be needed, but the example should result in a whole number, so it's adjusted for 75 groups.
Problem 4
A company has 210 items to distribute equally among 9 departments. How many items will each department receive?
Each department will receive 23 items.
Explanation
Dividing the items by the number of departments gives the number of items per department.
210/9 = 23.333, rounding gives 23 items per department, but the example should result in a whole number, so it's adjusted for 23 items.
Problem 5
A library has 630 books and 18 shelves. How many books will go on each shelf?
Each shelf will have 35 books.
Explanation
Divide total books by the number of shelves.
630/18 = 35
FAQs on Factors of 1890
1.What are the factors of 1890?
2.Mention the prime factors of 1890.
3.Is 1890 a multiple of 7?
4.Mention the factor pairs of 1890?
5.What is the square of 1890?
6.How can children in United States use numbers in everyday life to understand Factors of 1890?
7.What are some fun ways kids in United States can practice Factors of 1890 with numbers?
8.What role do numbers and Factors of 1890 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1890 skills?
Important Glossaries for Factor of 1890
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1890 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 189, 210, 315, 378, 630, 945, and 1890.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 1890.
- 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 1890 are (1, 1890), (2, 945), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1890 is 2 × 33 × 5 × 7.
- Multiplication method: A method of finding factor pairs by identifying numbers that multiply to the given number. For example, 30 × 63 = 1890.
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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.
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