126 LearnersLast updated on May 26th, 2025
Factors of -72
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 -72, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -72?
The numbers that divide -72 evenly are known as factors of -72.
A factor of -72 is a number that divides the number without remainder.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Negative factors of -72: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.
Prime factors of 72: 2 and 3.
Prime factorization of 72: 23 × 32.
The sum of factors of 72: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 = 192
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How to Find Factors of -72?
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 72. Identifying the numbers which are multiplied to get the number 72 is the multiplication method.
Step 1: Multiply 72 by 1, 72 × 1 = 72.
Step 2: Check for other numbers that give 72 after multiplying 2 × 36 = 72 3 × 24 = 72 4 × 18 = 72 6 × 12 = 72 8 × 9 = 72
Therefore, the positive factor pairs of 72 are: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9).
All these factor pairs result in 72.
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 72 by 1, 72 ÷ 1 = 72.
Step 2: Continue dividing 72 by the numbers until the remainder becomes 0.
72 ÷ 1 = 72
72 ÷ 2 = 36
72 ÷ 3 = 24
72 ÷ 4 = 18
72 ÷ 6 = 12
72 ÷ 8 = 9
Therefore, the factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
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 72 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 72 are 2 and 3.
The prime factorization of 72 is: 23 × 32.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 72 is divided by 2 to get 36.
Step 2: Now divide 36 by 2 to get 18.
Step 3: Then divide 18 by 2 to get 9.
Step 4: Divide 9 by 3 to get 3.
Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 72 is: 23 × 32.
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 72: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9).
Negative factor pairs of -72: (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), and (-8, -9).
Common Mistakes and How to Avoid Them in Factors of -72
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 72, 1 and 72 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 -72 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Sometimes, fractions might be mistakenly included. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 72/1.5 = 48, 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 72 are prime numbers.
For example, 2 and 3 are the prime factors of 72, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Skipping steps in factorization may lead to writing incorrect factors.
For example, not breaking 72 as 23 × 32 and missing key factors.
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Factors of -72 Examples
Problem 1
There are 9 friends and 72 cookies. How will they divide it equally?
They will get 8 cookies each.
Explanation
To divide the cookies equally, we need to divide the total cookies by the number of friends.
72/9 = 8
Problem 2
A field is rectangular, the length of the field is 9 meters, and the total area is 72 square meters. Find the width?
8 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width 72 = 9 × width
To find the value of width, we need to shift 9 to the left side.
72/9 = width
Width = 8.
Problem 3
There are 18 boxes and 72 candies. How many candies will be in each box?
Each box will have 4 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
72/18 = 4
Problem 4
In a class, there are 72 students and 6 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
72/6 = 12
Problem 5
72 apples need to be arranged in 8 baskets. How many apples will go in each basket?
Each of the baskets has 9 apples.
Explanation
Divide total apples by baskets.
72/8 = 9
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FAQs on Factors of -72
1.What are the factors of -72?
2.Mention the prime factors of 72.
3.Is 72 a multiple of 4?
4.Mention the factor pairs of 72?
5.What is the square of 72?
6.How can children in Bahrain use numbers in everyday life to understand Factors of -72?
7.What are some fun ways kids in Bahrain can practice Factors of -72 with numbers?
8.What role do numbers and Factors of -72 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of -72 skills?
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Important Glossaries for Factor of -72
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 72.
- 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 72 are (1, 72), (2, 36), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 72 is 23 × 32.
- Negative factors: The negative counterparts of the positive factors. For example, the negative factors of -72 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.
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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.
