123 LearnersLast updated on May 26th, 2025
Factors of 352
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 352, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 352?
The numbers that divide 352 evenly are known as factors of 352.
A factor of 352 is a number that divides the number without a remainder.
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.
Negative factors of 352: -1, -2, -4, -8, -11, -16, -22, -32, -44, -88, -176, and -352.
Prime factors of 352: 2 and 11.
Prime factorization of 352: 25 × 11.
The sum of factors of 352: 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 88 + 176 + 352 = 756
How to Find Factors of 352?
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 352. Identifying the numbers which are multiplied to get the number 352 is the multiplication method.
Step 1: Multiply 352 by 1, 352 × 1 = 352.
Step 2: Check for other numbers that give 352 after multiplying:
2 × 176 = 352
4 × 88 = 352
8 × 44 = 352
11 × 32 = 352
16 × 22 = 352
Therefore, the positive factor pairs of 352 are: (1, 352), (2, 176), (4, 88), (8, 44), (11, 32), (16, 22).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Divide the given numbers with whole numbers until the remainder becomes zero and list out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 352 by 1, 352 ÷ 1 = 352.
Step 2: Continue dividing 352 by numbers until the remainder becomes 0.
352 ÷ 1 = 352
352 ÷ 2 = 176
352 ÷ 4 = 88
352 ÷ 8 = 44
352 ÷ 11 = 32
352 ÷ 16 = 22
Therefore, the factors of 352 are: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
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 352 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
The prime factors of 352 are 2 and 11.
The prime factorization of 352 is: 25 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 352 is divided by 2 to get 176.
Step 2: Now divide 176 by 2 to get 88.
Step 3: Then divide 88 by 2 to get 44.
Step 4: Divide 44 by 2 to get 22.
Step 5: Divide 22 by 2 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 352 is: 2^5 × 11.
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 352: (1, 352), (2, 176), (4, 88), (8, 44), (11, 32), and (16, 22).
Negative factor pairs of 352: (-1, -352), (-2, -176), (-4, -88), (-8, -44), (-11, -32), and (-16, -22).
Common Mistakes and How to Avoid Them in Factors of 352
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 number. Always remember to include 1 and the number itself.
For example, in factors of 352, 1 and 352 are also factors.
Mistake 2
Missing Negative Factors
We usually mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 352 consist of -1, -2, -4, 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 352/1.5 = 234.666..., 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 352 are prime numbers.
For example, 2 and 11 are the prime factors of 352, but it has other factors like 4, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 352 as 2^5 × 11 and missing all the key factors.
Factors of 352 Examples
Problem 1
There are 11 teams and 352 players. How will they divide them equally?
Each team will get 32 players.
Explanation
To divide the players equally, we need to divide the total players by the number of teams.
352/11 = 32
Problem 2
A garden is rectangular, the width of the garden is 16 meters, and the total area is 352 square meters. Find the length.
22 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
352 = 16 × length
To find the value of length, we need to divide by 16.
352/16 = length Length = 22.
Problem 3
There are 8 baskets and 352 apples. How many apples will be in each basket?
Each basket will have 44 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
352/8 = 44
Problem 4
In a choir, there are 352 singers, and 16 groups. How many singers are there in each group?
There are 22 singers in each group.
Explanation
Dividing the singers by the total groups, we will get the number of singers in each group.
352/16 = 22
Problem 5
352 books need to be arranged in 32 shelves. How many books will go on each shelf?
Each of the shelves has 11 books.
Explanation
Divide total books by shelves.
352/32 = 11
FAQs on Factors of 352
1.What are the factors of 352?
2.Mention the prime factors of 352.
3.Is 352 a multiple of 11?
4.Mention the factor pairs of 352?
5.What is the square of 352?
6.How can children in Qatar use numbers in everyday life to understand Factors of 352?
7.What are some fun ways kids in Qatar can practice Factors of 352 with numbers?
8.What role do numbers and Factors of 352 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 352 skills?
Important Glossaries for Factors of 352
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.
- Prime factors: The factors which are prime numbers. For example, 2 and 11 are prime factors of 352.
- 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 352 are (1, 352), (2, 176), etc.
- Negative factors: Factors that are negative numbers dividing the given number without leaving a remainder. For example, -1, -2, -4, -8, etc., are negative factors of 352.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 352 is 25 × 11.
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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.
