206 LearnersLast updated on May 26th, 2025
Factors of 3136
Factors of 3136 are numbers that can divide 3136 completely without a remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 3136 and the different methods to find them.
What are the Factors of 3136?
The factors of 3136 are the numbers that divide 3136 evenly.
Positive Factors: These are the positive numbers that divide 3136 evenly.
Positive factors are 1, 2, 4, 8, 16, 49, 64, 98, 196, 256, 448, 784, 1568, and 3136.
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -8, -16, -49, -64, -98, -196, -256, -448, -784, -1568, -3136
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 3136 as the product.
Prime factors: 2, 7
Prime Factorization:
Prime factorization involves breaking 3136 into its prime factors.
It is expressed as 2⁶ × 7²
Table listing the factors of 3136
|
Positive Factors |
1, 2, 4, 8, 16, 49, 64, 98, 196, 256, 448, 784, 1568, 3136 |
|
Negative Factors |
-1, -2, -4, -8, -16, -49, -64, -98, -196, -256, -448, -784, -1568, -3136 |
|
Prime Factors |
2, 7 |
|
Prime Factorization |
2⁶ × 7² |
This breakdown helps in understanding the various factors of 3136, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 3136?
There are different methods to find the factors of 3136.
Methods to find the factors of 3136:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 3136 as their product.
Step 1: Find the pair of numbers whose product is 3136.
Step 2: The factors are those numbers, when multiplied, give 3136.
Step 3: Make a list of numbers whose product will be 3136.
A list of numbers whose products are 3136 is given below:
1 × 3136 = 3136
2 × 1568 = 3136
4 × 784 = 3136
8 × 392 = 3136
16 × 196 = 3136
49 × 64 = 3136
Thus, the factors of 3136 are 1, 2, 4, 8, 16, 49, 64, 98, 196, 256, 448, 784, 1568, 3136.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 3136 ÷ 1 = 3136
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 3136 are 1, 2, 4, 8, 16, 49, 64, 98, 196, 256, 448, 784, 1568, 3136.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number when it is simplified using the factors of that number and is expressed in the form of prime factors is the prime factorization of a number.
Prime Factors of 3136: Number 3136 has two prime factors.
Prime factors of 3136: 2, 7
To find the prime factors of 3136, we can divide 3136 with the prime numbers like 2 and 7 from the list of factors of 3136.
Step 1: Divide 3136 with the prime number 2
3136 ÷ 2 = 1568
Step 2: Divide 1568 with the prime number 2
1568 ÷ 2 = 784
Step 3: Divide 784 with the prime number 2
784 ÷ 2 = 392
Step 4: Divide 392 with the prime number 2
392 ÷ 2 = 196
Step 5: Divide 196 with the prime number 2
196 ÷ 2 = 98
Step 6: Divide 98 with the prime number 2
98 ÷ 2 = 49
Step 7: Divide 49 with the prime number 7
49 ÷ 7 = 7
Step 8: Divide 7 with the prime number 7
7 ÷ 7 = 1
Thus, the factors of 3136 are 1, 2, 4, 8, 16, 49, 64, 98, 196, 256, 448, 784, 1568, 3136.
Prime Factorization of 3136: Prime Factorization breaks down the prime factors of 3136:
Expressed as 2⁶ × 7²
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 3136 into its prime factors: 2⁶ × 7²
In this factor tree, each branch splits into prime factors.
Positive and Negative Factor Pairs of 3136
Factors of 3136 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs:
(1, 3136), (2, 1568), (4, 784), (8, 392), (16, 196), (49, 64)
Negative Factor Pairs:
(-1, -3136), (-2, -1568), (-4, -784), (-8, -392), (-16, -196), (-49, -64)
Common Mistakes and How to Avoid Them in Factors of 3136
Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Assuming 7 as the only factor of 3136
Since numbers divisible by 7 are multiples of 7, you might think 7 is the only factor of 3136. Remember, factors are numbers that can divide the given number completely. So, other numbers that can divide 3136 completely are 1, 2, 4, 8, 16, 49, 64, and more.
Factors of 3136 Examples
Problem 1
Can you check whether 75 and 25 are co-prime?
No, 75 and 25 are not co-prime.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 25: 1, 5, 25
Here, the GCF is 25. So 75 and 25 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 75 is a multiple of 7
No, 75 is not a multiple of 7.
Explanation
Multiples of 7 are numbers we get when 7 is multiplied by another number. No number can be multiplied by 7 to get 75 as the product.
Problem 3
Identify the perfect square from the factors of 75
The perfect square factor of 75 is 25 and the root is 5
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 5 is multiplied twice (5×5) we get the perfect square 25.
Problem 4
List the factors of 3136
The factors of 3136 are 1, 2, 4, 8, 16, 32, 49, 56, 112, 196, 256, 392, 784, 1568, 3136
Explanation
To find the factors of a number, divide the number by each of the numbers starting from 1 up to the number itself. For 3136, the factors are those numbers that divide 3136 exactly without leaving a remainder.
Problem 5
Is 3136 a perfect square?
Yes, 3136 is a perfect square.
Explanation
A perfect square is a number that is the square of an integer. The square root of 3136 is 56, as 56 × 56 = 3136. Therefore, 3136 is a perfect square.
FAQs on Factors of 3136
1.What are the factors of 3136?
2.How do you determine if a number is a factor of 3136?
3.What is the smallest factor of 3136?
4.What is the largest factor of 3136?
5.How many factors does 3136 have?
6.How many odd factors does 3136 have?
7.What factors go into 3136?
8.Do any perfect squares exist in the factors of 3136?
Important glossaries for the Factors of 3136
- Factor: Numbers that divide the given number completely without leaving a remainder.
- Prime Factor: Prime numbers that multiply together to give the original number.
- Prime Factorization: Expressing a number as the product of prime factors, written in exponential form.
- Multiple: Numbers that are obtained by multiplying the given number by integers.
- Perfect Square: A number that is the product of an integer multiplied by itself.
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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.
