113 LearnersLast updated on May 26th, 2025
Factors of 712
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 712, how they are used in real life, and tips to learn them quickly.
What are the Factors of 712?
The numbers that divide 712 evenly are known as factors of 712.
A factor of 712 is a number that divides the number without remainder.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712.
Negative factors of 712: -1, -2, -4, -8, -89, -178, -356, and -712.
Prime factors of 712: 2 and 89.
Prime factorization of 712: 2³ × 89.
The sum of factors of 712: 1 + 2 + 4 + 8 + 89 + 178 + 356 + 712 = 1350
How to Find Factors of 712?
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 712. Identifying the numbers which are multiplied to get the number 712 is the multiplication method.
Step 1: Multiply 712 by 1, 712 × 1 = 712.
Step 2: Check for other numbers that give 712 after multiplying
2 × 356 = 712
4 × 178 = 712
8 × 89 = 712
Therefore, the positive factor pairs of 712 are: (1, 712), (2, 356), (4, 178), (8, 89).
All these factor pairs result in 712.
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 712 by 1, 712 ÷ 1 = 712.
Step 2: Continue dividing 712 by the numbers until the remainder becomes 0.
712 ÷ 1 = 712
712 ÷ 2 = 356
712 ÷ 4 = 178
712 ÷ 8 = 89
Therefore, the factors of 712 are: 1, 2, 4, 8, 89, 178, 356, 712.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 712 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
712 ÷ 2 = 356
356 ÷ 2 = 178
178 ÷ 2 = 89
89 ÷ 89 = 1
The prime factors of 712 are 2 and 89.
The prime factorization of 712 is: 2³ × 89.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 712 is divided by 2 to get 356.
Step 2: Now divide 356 by 2 to get 178.
Step 3: Then divide 178 by 2 to get 89.
Here, 89 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 712 is: 2³ × 89.
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 712: (1, 712), (2, 356), (4, 178), (8, 89).
Negative factor pairs of 712: (-1, -712), (-2, -356), (-4, -178), (-8, -89).
Common Mistakes and How to Avoid Them in Factors of 712
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 712, 1 and 712 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 712 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 712/1.5 = 474.666, 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 712 are prime numbers.
For example, 2 and 89 are the prime factors of 712, but it has other factors like 4, 178.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 712 as 2³ × 89 and missing all the key factors.
Factors of 712 Examples
Problem 1
There are 8 friends and 712 marbles. How will they divide it equally?
They will get 89 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
712/8 = 89
Problem 2
A field is rectangular, the length of the field is 4 meters and the total area is 712 square meters. Find the width?
178 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
712 = 4 × width
To find the value of the width, we need to shift 4 to the left side.
712/4 = width
Width = 178.
Problem 3
There are 2 trucks and 712 boxes. How many boxes will be in each truck?
Each truck will have 356 boxes.
Explanation
To find the boxes in each truck, divide the total boxes by the trucks.
712/2 = 356
Problem 4
In a company, there are 712 employees, and 4 departments. How many employees are there in each department?
There are 178 employees in each department.
Explanation
Dividing the employees by the total departments, we will get the number of employees in each department.
712/4 = 178
Problem 5
712 pages need to be organized into 89 folders. How many pages will go in each folder?
Each of the folders has 8 pages.
Explanation
Divide total pages by the folders.
712/89 = 8
FAQs on Factors of 712
1.What are the factors of 712?
2.Mention the prime factors of 712.
3.Is 712 a multiple of 4?
4.Mention the factor pairs of 712?
5.What is the square of 712?
Important Glossaries for Factor of 712
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712.
- Prime factors: The factors which are prime numbers. For example, 2 and 89 are prime factors of 712.
- 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 712 are (1, 712), (2, 356), etc.
- Multiplication Method: A method to find factors by identifying pairs of numbers that multiply to give the target number.
- Division Method: A technique to find factors by dividing the number by integers until the remainder is zero.
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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.
