127 LearnersLast updated on May 26th, 2025
Factors of 1950
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 1950, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1950?
The numbers that divide 1950 evenly are known as factors of 1950.
A factor of 1950 is a number that divides the number without a remainder.
The factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 150, 195, 260, 390, 650, 975, and 1950.
Negative factors of 1950: -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -150, -195, -260, -390, -650, -975, and -1950.
Prime factors of 1950: 2, 3, 5, and 13.
Prime factorization of 1950: 2 × 3 × 52 × 13.
The sum of factors of 1950: 1 + 2 + 3 + 5 + 6 + 10 + 13 + 15 + 26 + 30 + 39 + 65 + 78 + 130 + 150 + 195 + 260 + 390 + 650 + 975 + 1950 = 6207.
How to Find Factors of 1950?
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 1950. Identifying the numbers which are multiplied to get the number 1950 is the multiplication method.
Step 1: Multiply 1950 by 1, 1950 × 1 = 1950.
Step 2: Check for other numbers that give 1950 after multiplying (2 × 975 = 1950) (3 × 650 = 1950) (5 × 390 = 1950) (6 × 325 = 1950) (10 × 195 = 1950) (13 × 150 = 1950)
Therefore, the positive factor pairs of 1950 are: (1, 1950), (2, 975), (3, 650), (5, 390), (6, 325), (10, 195), (13, 150).
All these factor pairs result in 1950.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1950 by 1, 1950 ÷ 1 = 1950.
Step 2: Continue dividing 1950 by the numbers until the remainder becomes 0.
1950 ÷ 1 = 1950
1950 ÷ 2 = 975
1950 ÷ 3 = 650
1950 ÷ 5 = 390
1950 ÷ 6 = 325
1950 ÷ 10 = 195
1950 ÷ 13 = 150
Therefore, the factors of 1950 are: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 150, 195, 260, 390, 650, 975, and 1950.
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 1950 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1950 ÷ 2 = 975
975 ÷ 3 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 1950 are 2, 3, 5, and 13. The prime factorization of 1950 is: (2 × 3 0215 52 × 13).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1950 is divided by 2 to get 975.
Step 2: Now divide 975 by 3 to get 325.
Step 3: Then divide 325 by 5 to get 65.
Step 4: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1950 is: (2 × 3 × 52 × 13).
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 1950: (1, 1950), (2, 975), (3, 650), (5, 390), (6, 325), (10, 195), (13, 150).
Negative factor pairs of 1950: (-1, -1950), (-2, -975), (-3, -650), (-5, -390), (-6, -325), (-10, -195), (-13, -150).
Common Mistakes and How to Avoid Them in Factors of 1950
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 1950, 1 and 1950 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1950 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 1950/1.5 = 1300, 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 1950 are prime numbers.
For example, 2, 3, 5, and 13 are the prime factors of 1950, but it has other factors like 6, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1950 as (2 × 3 × 52 × 13) and missing all the key factors.
Factors of 1950 Examples
Problem 1
A company has 1950 promotional items to distribute equally among 13 branches. How many items will each branch receive?
Each branch will receive 150 items.
Explanation
To divide the items equally, we need to divide the total items by the number of branches.
1950/13 = 150
Problem 2
A rectangular plot has a length of 65 meters and a total area of 1950 square meters. What is the width of the plot?
30 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1950 = 65 × width
To find the value of width, we need to shift 65 to the left side.
1950/65 = width
Width = 30.
Problem 3
A warehouse has 26 pallets and a total of 1950 boxes. How many boxes are on each pallet?
Each pallet has 75 boxes.
Explanation
To find the boxes on each pallet, divide the total boxes by the number of pallets.
1950/26 = 75
Problem 4
A team needs to split into groups of 15 members each, with a total of 1950 participants. How many groups will there be?
There will be 130 groups.
Explanation
Dividing participants by the number of members per group, we will get the number of groups.
1950/15 = 130
Problem 5
A library has 1950 books and wants to arrange them equally in 5 sections. How many books will go in each section?
Each section will have 390 books.
Explanation
Divide total books by the number of sections.
1950/5 = 390
FAQs on Factors of 1950
1.What are the factors of 1950?
2.Mention the prime factors of 1950.
3.Is 1950 a multiple of 5?
4.Mention the factor pairs of 1950?
5.What is the square of 1950?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 1950?
7.What are some fun ways kids in Indonesia can practice Factors of 1950 with numbers?
8.What role do numbers and Factors of 1950 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 1950 skills?
Important Glossaries for Factor of 1950
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 150, 195, 260, 390, 650, 975, and 1950.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 1950.
- 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 1950 are (1, 1950), (2, 975), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1950 is (2 × 3 × 5^2 × 13).
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -150, -195, -260, -390, -650, -975, and -1950 are the negative factors of 1950.
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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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