Factors of 3200

The factors of 3200 are the numbers that divide 3200 evenly.
The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, and 3200.
 

Positive Factors: These are the positive numbers that divide 3200 evenly.
Positive factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, 3200
 

Negative Factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -125, -160, -200, -250, -400, -800, -1600, -3200
 

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 3200 as the product.
Prime factors of 3200: 2, 5
 

Prime Factorization: Prime factorization involves breaking down 3200 into its prime factors.
It is expressed as:
3200 = 2⁷ × 5²

Table listing the factors of 3200

This breakdown helps in understanding the various factors of 3200, 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 3200.

Methods to find the factors of 3200:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
 

The multiplication method finds the pair of factors that give 3200 as their product.
 

Step 1: Find the pair of numbers whose product is 3200.
 

Step 2: The factors are those numbers, when multiplied, give 3200.
 

Step 3: Make a list of numbers whose product will be 3200.

A list of numbers whose products are 3200 is given below:

• 1 × 3200 = 3200
• 2 × 1600 = 3200
• 4 × 800 = 3200
• 5 × 640 = 3200
• 8 × 400 = 3200
• 10 × 320 = 3200
• 16 × 200 = 3200
• 20 × 160 = 3200
• 25 × 128 = 3200
• 32 × 100 = 3200
• 40 × 80 = 3200
• 50 × 64 = 3200

Thus, the factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, and 3200.

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: 3200÷1=3200
 

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 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 800, 1600, 3200.

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 3200: Number 3200 has only two prime factors.
Prime factors of 3200: 2, 5
To find the prime factors of 3200, we can divide 3200 with the prime numbers like 2 and 5 from the list of factors of 3200.
 

Step 1: Divide 3200 with the prime number 2
3200 ÷ 2 = 1600
Step 2: Divide 1600 with the prime number 2
1600 ÷ 2 = 800
Step 3: Divide 800 with the prime number 2
800 ÷ 2 = 400
Step 4: Divide 400 with the prime number 2
400 ÷ 2 = 200
Step 5: Divide 200 with the prime number 2
200 ÷ 2 = 100
Step 6: Divide 100 with the prime number 2
100 ÷ 2 = 50
Step 7: Divide 50 with the prime number 2
50 ÷ 2 = 25
Step 8: Divide 25 with the prime number 5
25 ÷ 5 = 5
Step 9: Divide 5 with the prime number 5
5 ÷ 5 = 1

Prime Factorization of 3200:
Prime Factorization breaks down the prime factors of 3200:
3200 = 2⁷ × 5²

The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 3200 into its prime factors: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5

In this factor tree, each branch splits into prime factors.

Positive and Negative Factor Pairs of 3200

Factors of 3200 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: (1,3200), (2,1600), (4,800), (5,640), (8,400), (10,320), (16,200), (20,160), (25,128), (32,100), (40,80), (50,64), (125,25), (160,20), (200,16), (250,12), (400,8), (800,4), (1600,2)
 

Negative Factor Pairs: (-1,-3200), (-2,-1600), (-4,-800), (-5,-640), (-8,-400), (-10,-320), (-16,-200), (-20,-160), (-25,-128), (-32,-100), (-40,-80), (-50,-64), (-125,-25), (-160,-20), (-200,-16), (-250,-12), (-400,-8), (-800,-4), (-1600,-2)

• Factor: A number that divides another number completely without leaving a remainder.
   
• Prime Factor: A prime number that divides the given number exactly.
   
• Prime Factorization: The expression of a number as the product of its prime factors.
   
• Multiplication Method: A method used to find factors by multiplying pairs of numbers that result in the given number.
   
• Factor Tree: A diagram that visually represents the prime factorization of a number by breaking it down into its prime factors.