115 LearnersLast updated on May 26th, 2025
Factors of 1952
Factors are the numbers that divide any given number evenly without a 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 1952, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1952?
The numbers that divide 1952 evenly are known as factors of 1952.
A factor of 1952 is a number that divides the number without a remainder.
The factors of 1952 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976, and 1952.
Negative factors of 1952: -1, -2, -4, -8, -16, -61, -122, -244, -488, -976, and -1952.
Prime factors of 1952: 2 and 61.
Prime factorization of 1952: 24 × 61.
The sum of factors of 1952: 1 + 2 + 4 + 8 + 16 + 61 + 122 + 244 + 488 + 976 + 1952 = 3874
How to Find Factors of 1952?
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 1952. Identifying the numbers which are multiplied to get the number 1952 is the multiplication method.
Step 1: Multiply 1952 by 1, 1952 × 1 = 1952.
Step 2: Check for other numbers that give 1952 after multiplying
2 × 976 = 1952
4 × 488 = 1952
8 × 244 = 1952
16 × 122 = 1952
61 × 32 = 1952
Therefore, the positive factor pairs of 1952 are: (1, 1952), (2, 976), (4, 488), (8, 244), (16, 122), and (32, 61).
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 1952 by 1, 1952 ÷ 1 = 1952.
Step 2: Continue dividing 1952 by the numbers until the remainder becomes 0.
1952 ÷ 1 = 1952
1952 ÷ 2 = 976
1952 ÷ 4 = 488
1952 ÷ 8 = 244
1952 ÷ 16 = 122
1952 ÷ 32 = 61
Therefore, the factors of 1952 are: 1, 2, 4, 8, 16, 32, 61, 122, 244, 488, 976, and 1952.
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 1952 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1952 ÷ 2 = 976
976 ÷ 2 = 488
488 ÷ 2 = 244
244 ÷ 2 = 122
122 ÷ 2 = 61
61 ÷ 61 = 1
The prime factors of 1952 are 2 and 61.
The prime factorization of 1952 is: 24 × 61.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1952 is divided by 2 to get 976.
Step 2: Now divide 976 by 2 to get 488.
Step 3: Then divide 488 by 2 to get 244.
Step 4: Divide 244 by 2 to get 122.
Step 5: Divide 122 by 2 to get 61. Here, 61 is a prime number that cannot be divided anymore. So, the prime factorization of 1952 is: 24 × 61.
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 1952: (1, 1952), (2, 976), (4, 488), (8, 244), (16, 122), and (32, 61).
Negative factor pairs of 1952: (-1, -1952), (-2, -976), (-4, -488), (-8, -244), (-16, -122), and (-32, -61).
Common Mistakes and How to Avoid Them in Factors of 1952
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 factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 1952, 1 and 1952 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 1952 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1952/1.5 = 1301.333, 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 1952 are prime numbers.
For example, 2 and 61 are the prime factors of 1952, but it has other factors like 4, 16.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1952 as 2^4 × 61 and missing all the key factors.
Factors of 1952 Examples
Problem 1
There are 16 students and 1952 candies. How will they divide it equally?
They will get 122 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1952/16 = 122
Problem 2
A garden is rectangular, the width of the garden is 32 meters and the total area is 1952 square meters. Find the length?
61 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1952 = 32 × length
To find the value of length, we need to shift 32 to the left side.
1952/32 = length
Length = 61.
Problem 3
There are 4 buses and 1952 passengers. How many passengers will be in each bus?
Each bus will have 488 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the buses.
1952/4 = 488
Problem 4
In a conference, there are 1952 attendees, and 8 groups. How many attendees are there in each group?
There are 244 attendees in each group.
Explanation
Dividing the attendees by the total groups, we will get the number of attendees in each group.
1952/8 = 244
Problem 5
1952 books need to be arranged in 2 sections. How many books will go in each section?
Each of the sections has 976 books.
Explanation
Divide total books by sections.
1952/2 = 976
FAQs on Factors of 1952
1.What are the factors of 1952?
2.Mention the prime factors of 1952.
3.Is 1952 a multiple of 8?
4.Mention the factor pairs of 1952?
5.What is the square of 1952?
Important Glossaries for Factor of 1952
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1952 are 1, 2, 4, 8, 16, 32, 61, 122, 244, 488, 976, and 1952.
- Prime factors: The factors which are prime numbers. For example, 2 and 61 are prime factors of 1952.
- 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 1952 are (1, 1952), (2, 976), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 1952 is expressed as 24 × 61.
- Multiple: A number that can be divided by another number without a remainder. For example, 1952 is a multiple of 8.
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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
: She loves to read number jokes and games.
