120 LearnersLast updated on May 26th, 2025
Factors of 1949
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 1949, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1949?
The numbers that divide 1949 evenly are known as factors of 1949.
A factor of 1949 is a number that divides the number without remainder.
The factors of 1949 are 1, 37, 53, and 1949.
Negative factors of 1949: -1, -37, -53, and -1949.
Prime factors of 1949: 37 and 53.
Prime factorization of 1949: 37 × 53.
The sum of factors of 1949: 1 + 37 + 53 + 1949 = 2040
How to Find Factors of 1949?
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 1949. Identifying the numbers which are multiplied to get the number 1949 is the multiplication method.
Step 1: Multiply 1949 by 1, 1949 × 1 = 1949.
Step 2: Check for other numbers that give 1949 after multiplying: 37 × 53 = 1949
Therefore, the positive factor pairs of 1949 are: (1, 1949) and (37, 53).
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 a whole number as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1949 by 1, 1949 ÷ 1 = 1949.
Step 2: Continue dividing 1949 by the numbers until the remainder becomes 0.
1949 ÷ 1 = 1949
1949 ÷ 37 = 53
1949 ÷ 53 = 37
Therefore, the factors of 1949 are: 1, 37, 53, and 1949.
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 1949 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1949 ÷ 37 = 53
53 ÷ 53 = 1
The prime factors of 1949 are 37 and 53.
The prime factorization of 1949 is: 37 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1949 is divided by 37 to get 53.
Step 2: Now divide 53 by 53 to get 1. Here, 53 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1949 is: 37 × 53.
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 1949: (1, 1949) and (37, 53).
Negative factor pairs of 1949: (-1, -1949) and (-37, -53).
Common Mistakes and How to Avoid Them in Factors of 1949
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
People 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 1949, 1 and 1949 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 1949 consist of -1, -37, -53, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1949/1.5 = 1299.333, 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 1949 are prime numbers.
For example, 37 and 53 are the prime factors of 1949, but it has other factors like 1 and 1949.
Mistake 5
Mistake in Factorization
People might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1949 as 37 × 53 and missing all the key factors.
Factors of 1949 Examples
Problem 1
There are 37 students and 1949 candies. How will they divide it equally?
They will get 53 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1949/37 = 53
Problem 2
A garden is rectangular, the length of the garden is 37 meters and the total area is 1949 square meters. Find the width?
53 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1949 = 37 × width
To find the value of width, we need to shift 37 to the left side.
1949/37 = width
Width = 53.
Problem 3
There are 53 boxes and 1949 marbles. How many marbles will be in each box?
Each box will have 37 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1949/53 = 37
Problem 4
In a tournament, there are 1949 participants and 37 teams. How many participants are there in each team?
There are 53 participants in each team.
Explanation
Dividing the participants by the total teams, we will get the number of participants in each team.
1949/37 = 53
Problem 5
1949 books need to be arranged in 53 shelves. How many books will go on each shelf?
Each of the shelves has 37 books.
Explanation
Divide total books by shelves.
1949/53 = 37
FAQs on Factors of 1949
1.What are the factors of 1949?
2.Mention the prime factors of 1949.
3.Is 1949 a multiple of 37?
4.Mention the factor pairs of 1949?
5.What is the square of 1949?
6.How can children in Canada use numbers in everyday life to understand Factors of 1949?
7.What are some fun ways kids in Canada can practice Factors of 1949 with numbers?
8.What role do numbers and Factors of 1949 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1949 skills?
Important Glossaries for Factors of 1949
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1949 are 1, 37, 53, and 1949.
- Prime factors: The factors which are prime numbers. For example, 37 and 53 are prime factors of 1949.
- 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 1949 are (1, 1949) and (37, 53).
- Negative factors: Factors that are negative numbers. For example, -1, -37, -53, and -1949 are negative factors of 1949.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1949 is 37 × 53.
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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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