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

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.

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
 

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.
 

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.
 

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
 

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)
 

• 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.