103 LearnersLast updated on May 26th, 2025
Factors of 272
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 272, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 272?
The numbers that divide 272 evenly are known as factors of 272.
A factor of 272 is a number that divides the number without remainder.
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, and 272.
Negative factors of 272: -1, -2, -4, -8, -16, -17, -34, -68, -136, and -272.
Prime factors of 272: 2 and 17.
Prime factorization of 272: 2^4 × 17.
The sum of factors of 272: 1 + 2 + 4 + 8 + 16 + 17 + 34 + 68 + 136 + 272 = 558
How to Find Factors of 272?
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 272. Identifying the numbers which are multiplied to get the number 272 is the multiplication method.
Step 1: Multiply 272 by 1, 272 × 1 = 272.
Step 2: Check for other numbers that give 272 after multiplying
2 × 136 = 272
4 × 68 = 272
8 × 34 = 272
16 × 17 = 272
Therefore, the positive factor pairs of 272 are: (1, 272), (2, 136), (4, 68), (8, 34), (16, 17).
All these factor pairs result in 272.
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 272 by 1, 272 ÷ 1 = 272.
Step 2: Continue dividing 272 by the numbers until the remainder becomes 0.
272 ÷ 1 = 272
272 ÷ 2 = 136
272 ÷ 4 = 68
272 ÷ 8 = 34
272 ÷ 16 = 17
Therefore, the factors of 272 are: 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.
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 272 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
272 ÷ 2 = 136
136 ÷ 2 = 68
68 ÷ 2 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1
The prime factors of 272 are 2 and 17.
The prime factorization of 272 is: 2^4 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 272 is divided by 2 to get 136.
Step 2: Now divide 136 by 2 to get 68.
Step 3: Then divide 68 by 2 to get 34.
Step 4: Divide 34 by 2 to get 17. Here, 17 is the smallest prime number, that cannot be divided further. So, the prime factorization of 272 is: 24 × 17.
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 272: (1, 272), (2, 136), (4, 68), (8, 34), and (16, 17).
Negative factor pairs of 272: (-1, -272), (-2, -136), (-4, -68), (-8, -34), and (-16, -17).
Common Mistakes and How to Avoid Them in Factors of 272
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 word. Always remember to include 1 and the number itself.
For example, in factors of 272, 1 and 272 are also factors.
Factors of 272 Examples
Problem 1
There are 17 classrooms and 272 chairs. How will they arrange them equally?
They will place 16 chairs in each classroom.
Explanation
To arrange the chairs equally, we need to divide the total chairs with the number of classrooms.
272/17 = 16
Problem 2
A stage is rectangular, the length of the stage is 8 meters and the total area is 272 square meters. Find the width?
34 meters.
Explanation
To find the width of the stage, we use the formula,
Area = length × width
272 = 8 × width
To find the value of width, we need to shift 8 to the left side.
272/8 = width
Width = 34.
Problem 3
There are 34 baskets and 272 apples. How many apples will be in each basket?
Each basket will have 8 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
272/34 = 8
Problem 4
In a stadium, there are 272 seats, and 16 sections. How many seats are there in each section?
There are 17 seats in each section.
Explanation
Dividing the seats with the total sections, we will get the number of seats in each section.
272/16 = 17
Problem 5
272 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 68 books.
Explanation
Divide total books with shelves.
272/4 = 68
FAQs on Factors of 272
1.What are the factors of 272?
2.Mention the prime factors of 272.
3.Is 272 a multiple of 8?
4.Mention the factor pairs of 272.
5.What is the square of 272?
6.How can children in Australia use numbers in everyday life to understand Factors of 272?
7.What are some fun ways kids in Australia can practice Factors of 272 with numbers?
8.What role do numbers and Factors of 272 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 272 skills?
Important Glossaries for Factors of 272
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, and 272.
- Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of 272.
- 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 272 are (1, 272), (2, 136), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 272 is 24 × 17.
- Multiple: A number that can be divided by another number without a remainder. For example, 272 is a multiple of 8.
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About BrightChamps in Australia
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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