# Factors of 25600

Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, and 25600

#### How to find factors of a number

 1.   Find factors of 25600 using Division Method 2.   Find factors of 25600 using Prime Factorization 3.   Find factors of 25600 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 25600

• Divide 25600 by 1: 25600 ÷ 1 : Remainder = 0
• Divide 25600 by 2: 25600 ÷ 2 : Remainder = 0
• Divide 25600 by 4: 25600 ÷ 4 : Remainder = 0
• Divide 25600 by 5: 25600 ÷ 5 : Remainder = 0
• Divide 25600 by 8: 25600 ÷ 8 : Remainder = 0
• Divide 25600 by 10: 25600 ÷ 10 : Remainder = 0
• Divide 25600 by 16: 25600 ÷ 16 : Remainder = 0
• Divide 25600 by 20: 25600 ÷ 20 : Remainder = 0
• Divide 25600 by 25: 25600 ÷ 25 : Remainder = 0
• Divide 25600 by 32: 25600 ÷ 32 : Remainder = 0
• Divide 25600 by 40: 25600 ÷ 40 : Remainder = 0
• Divide 25600 by 50: 25600 ÷ 50 : Remainder = 0
• Divide 25600 by 64: 25600 ÷ 64 : Remainder = 0
• Divide 25600 by 80: 25600 ÷ 80 : Remainder = 0
• Divide 25600 by 100: 25600 ÷ 100 : Remainder = 0
• Divide 25600 by 128: 25600 ÷ 128 : Remainder = 0
• Divide 25600 by 160: 25600 ÷ 160 : Remainder = 0
• Divide 25600 by 200: 25600 ÷ 200 : Remainder = 0
• Divide 25600 by 256: 25600 ÷ 256 : Remainder = 0
• Divide 25600 by 320: 25600 ÷ 320 : Remainder = 0
• Divide 25600 by 400: 25600 ÷ 400 : Remainder = 0
• Divide 25600 by 512: 25600 ÷ 512 : Remainder = 0
• Divide 25600 by 640: 25600 ÷ 640 : Remainder = 0
• Divide 25600 by 800: 25600 ÷ 800 : Remainder = 0
• Divide 25600 by 1024: 25600 ÷ 1024 : Remainder = 0
• Divide 25600 by 1280: 25600 ÷ 1280 : Remainder = 0
• Divide 25600 by 1600: 25600 ÷ 1600 : Remainder = 0
• Divide 25600 by 2560: 25600 ÷ 2560 : Remainder = 0
• Divide 25600 by 3200: 25600 ÷ 3200 : Remainder = 0
• Divide 25600 by 5120: 25600 ÷ 5120 : Remainder = 0
• Divide 25600 by 6400: 25600 ÷ 6400 : Remainder = 0
• Divide 25600 by 12800: 25600 ÷ 12800 : Remainder = 0
• Divide 25600 by 25600: 25600 ÷ 25600 : Remainder = 0

Hence, Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, and 25600

#### 2. Steps to find factors of 25600 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 25600 using the division method, follow these steps:

• Step 1. Start dividing 25600 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 25600, which is 2. Divide 25600 by 2 to obtain the quotient (12800).
25600 ÷ 2 = 12800
• Step 3. Repeat step 1 with the obtained quotient (12800).
12800 ÷ 2 = 6400
6400 ÷ 2 = 3200
3200 ÷ 2 = 1600
1600 ÷ 2 = 800
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 25600 is, 25600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 25600 as shown below:

So, the prime factorization of 25600 is, 25600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5.

#### 3. Find factors of 25600 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 25600 would be the two numbers which, when multiplied, give 25600 as the result.

The following table represents the calculation of factors of 25600 in pairs:

Factor Pair Pair Factorization
1 and 25600 1 x 25600 = 25600
2 and 12800 2 x 12800 = 25600
4 and 6400 4 x 6400 = 25600
5 and 5120 5 x 5120 = 25600
8 and 3200 8 x 3200 = 25600
10 and 2560 10 x 2560 = 25600
16 and 1600 16 x 1600 = 25600
20 and 1280 20 x 1280 = 25600
25 and 1024 25 x 1024 = 25600
32 and 800 32 x 800 = 25600
40 and 640 40 x 640 = 25600
50 and 512 50 x 512 = 25600
64 and 400 64 x 400 = 25600
80 and 320 80 x 320 = 25600
100 and 256 100 x 256 = 25600
128 and 200 128 x 200 = 25600
160 and 160 160 x 160 = 25600

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 25600. They are called negative pair factors.

Hence, the negative pairs of 25600 would be ( -1 , -25600 ) , ( -2 , -12800 ) , ( -4 , -6400 ) , ( -5 , -5120 ) , ( -8 , -3200 ) , ( -10 , -2560 ) , ( -16 , -1600 ) , ( -20 , -1280 ) , ( -25 , -1024 ) , ( -32 , -800 ) , ( -40 , -640 ) , ( -50 , -512 ) , ( -64 , -400 ) , ( -80 , -320 ) , ( -100 , -256 ) , ( -128 , -200 ) and ( -160 , -160 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 25600 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 25600.
• Every number is a factor of zero (0), since 25600 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600 are exact divisors of 25600.
• Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600. Each factor divides 25600 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600 are all less than or equal to 25600.

• Is 25600 a perfect square?

Yes 25600 is a perfect square.

• What are factors of 25600?

Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600.

• Which is greatest factor of 25600?

The greatest factor of 25600 is 12800.

• What is the sum of all factors of 25600?

The sum of all factors of 25600 is 63457.

• What are multiples of 25600?

First five multiples of 25600 are 51200, 76800, 102400, 128000.

• What is the greatest prime factors of 25600?

The greatest prime factor of 25600 is 5.

• What are six multiples of 25600?

First five multiples of 25600 are 51200, 76800, 102400, 128000, 153600, 179200.

• What is prime factorization of 25600?

Prime factorization of 25600 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5.

• Is 25600 a whole number?

Yes 25600 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 25600? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -256, -320, -400, -512, -640, -800, -1024, -1280, -1600, -2560, -3200, -5120, -6400, -12800, -25600.

Can you help Sammy find out the product of the odd factors of 25600?

Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600.
Odd factors of 25600 are 1, 5, 25.
Hence product of odd factors of 25600 is; 1 x 5 x 25 = 125.

Joey wants to write all the prime factors of 25600 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 25600 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5.
So in exponential form it can be written as 210 x 52.

How many factors are there for 25600?

Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600.
So there are in total 33 factors.

Kevin has been asked to write 32 factor(s) of 25600. Can you predict the answer?

32 factor(s) of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800.

Sammy is puzzled while calculating the prime factors of 25600. Can you help him find them?

Factors of 25600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 512, 640, 800, 1024, 1280, 1600, 2560, 3200, 5120, 6400, 12800, 25600.
Prime factors of 25600 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5

What is prime factorization of 25600?

Prime factorization of 25600 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 210 x 52.