Factors of 6400

The factors of 6400 are the numbers that can divide 6400 completely without any remainder.
The factors of 6400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.
 

Positive Factors: The positive factors of 6400 are all the numbers that can divide 6400 evenly. These are:
Positive factors of 6400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, 6400.
 

Negative Factors: These are the negative counterparts of the positive factors.
Negative factors of 6400: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -256, -400, -512, -800, -1600, -6400.
 

Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 6400 as the product.
Prime factors of 6400: 2, 5.
 

Prime Factorization: Prime factorization involves breaking 6400 into its prime factors. The prime factorization of 6400 is expressed as:
Prime Factorization of 6400: 2⁷ × 5².

Table listing the factors of 6400

This breakdown helps in understanding the various factors of 6400, whether they are positive or negative, as well as how prime factorization works for this number.

There are several methods to find the factors of 6400:

Methods to find the factors of 6400:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree

The multiplication method involves finding the pair of numbers whose product is 6400.
 

Step 1: Find the pair of numbers whose product is 6400.
 

Step 2: The factors are those numbers that, when multiplied, give 6400.
 

Step 3: Make a list of numbers whose product will be 6400.
A list of numbers whose products are 6400 is given below:

• 1 × 6400 = 6400
• 2 × 3200 = 6400
• 4 × 1600 = 6400
• 5 × 1280 = 6400
• 8 × 800 = 6400
• 10 × 640 = 6400
• 16 × 400 = 6400
• 20 × 320 = 6400
• 25 × 256 = 6400
• 32 × 200 = 6400
• 40 × 160 = 6400
• 50 × 128 = 6400
• 64 × 100 = 6400
• 80 × 80 = 6400

Thus, the factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.
 

The division method finds the numbers that completely divide the given number. The steps are as follows:
 

Step 1: Since every number is divisible by 1, 1 will always be a factor.
 

Step 2: Move to the next integer. The factors of 6400 include the number that is used to divide and the quotient.

Thus, the factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 400, 512, 800, 1600, and 6400.

Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number and expressed in the form of prime factors, is its prime factorization.
 

Prime Factors of 6400: 2, 5.
To find the prime factors of 6400, we can divide 6400 by prime numbers like 2 and 5 from the list of factors of 6400.
 

Step 1: Divide 6400 by the prime number 2:

• 6400 ÷ 2 = 3200
• 3200 ÷ 2 = 1600
• 1600 ÷ 2 = 800
• 800 ÷ 2 = 400
• 400 ÷ 2 = 200
• 200 ÷ 2 = 100
• 100 ÷ 2 = 50
• 50 ÷ 2 = 25
   

Step 2: Now divide 25 by the prime number 5:

• 25 ÷ 5 = 5
• 5 ÷ 5 = 1
   

Prime Factorization of 6400: 6400 = 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 6400 into its prime factors: 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 6400

Factors of 6400 can be written in both positive and negative pairs. These are like team members, and their product will be equal to the number 6400.
 

Positive Factor Pairs:
(1, 6400), (2, 3200), (4, 1600), (5, 1280), (8, 800), (10, 640), (16, 400), (20, 320), (25, 256), (32, 200), (40, 160), (50, 128), (64, 100), (80, 80).
 

Negative Factor Pairs:
(-1, -6400), (-2, -3200), (-4, -1600), (-5, -1280), (-8, -800), (-10, -640), (-16, -400), (-20, -320), (-25, -256), (-32, -200), (-40, -160), (-50, -128), (-64, -100), (-80, -80).
 

• Factors: Numbers that can divide a given number completely without leaving a remainder.

• Prime Factors: Prime numbers that, when multiplied together, give the original number.

• Prime Factorization: Breaking down a number into its prime factors.

• Perfect Square: A number that is the product of a number multiplied by itself.

• Multiple: Numbers we get when a number is multiplied by any integer.