# Factors of 1600

Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, and 1600

#### How to find factors of a number

 1.   Find factors of 1600 using Division Method 2.   Find factors of 1600 using Prime Factorization 3.   Find factors of 1600 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1600

• Divide 1600 by 1: 1600 ÷ 1 : Remainder = 0
• Divide 1600 by 2: 1600 ÷ 2 : Remainder = 0
• Divide 1600 by 4: 1600 ÷ 4 : Remainder = 0
• Divide 1600 by 5: 1600 ÷ 5 : Remainder = 0
• Divide 1600 by 8: 1600 ÷ 8 : Remainder = 0
• Divide 1600 by 10: 1600 ÷ 10 : Remainder = 0
• Divide 1600 by 16: 1600 ÷ 16 : Remainder = 0
• Divide 1600 by 20: 1600 ÷ 20 : Remainder = 0
• Divide 1600 by 25: 1600 ÷ 25 : Remainder = 0
• Divide 1600 by 32: 1600 ÷ 32 : Remainder = 0
• Divide 1600 by 40: 1600 ÷ 40 : Remainder = 0
• Divide 1600 by 50: 1600 ÷ 50 : Remainder = 0
• Divide 1600 by 64: 1600 ÷ 64 : Remainder = 0
• Divide 1600 by 80: 1600 ÷ 80 : Remainder = 0
• Divide 1600 by 100: 1600 ÷ 100 : Remainder = 0
• Divide 1600 by 160: 1600 ÷ 160 : Remainder = 0
• Divide 1600 by 200: 1600 ÷ 200 : Remainder = 0
• Divide 1600 by 320: 1600 ÷ 320 : Remainder = 0
• Divide 1600 by 400: 1600 ÷ 400 : Remainder = 0
• Divide 1600 by 800: 1600 ÷ 800 : Remainder = 0
• Divide 1600 by 1600: 1600 ÷ 1600 : Remainder = 0

Hence, Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, and 1600

#### 2. Steps to find factors of 1600 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 1600 using the division method, follow these steps:

• Step 1. Start dividing 1600 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 1600, which is 2. Divide 1600 by 2 to obtain the quotient (800).
1600 ÷ 2 = 800
• Step 3. Repeat step 1 with the obtained quotient (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 1600 is, 1600 = 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 1600 as shown below:

So, the prime factorization of 1600 is, 1600 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5.

#### 3. Find factors of 1600 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 1600 would be the two numbers which, when multiplied, give 1600 as the result.

The following table represents the calculation of factors of 1600 in pairs:

Factor Pair Pair Factorization
1 and 1600 1 x 1600 = 1600
2 and 800 2 x 800 = 1600
4 and 400 4 x 400 = 1600
5 and 320 5 x 320 = 1600
8 and 200 8 x 200 = 1600
10 and 160 10 x 160 = 1600
16 and 100 16 x 100 = 1600
20 and 80 20 x 80 = 1600
25 and 64 25 x 64 = 1600
32 and 50 32 x 50 = 1600
40 and 40 40 x 40 = 1600

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 1600. They are called negative pair factors.

Hence, the negative pairs of 1600 would be ( -1 , -1600 ) , ( -2 , -800 ) , ( -4 , -400 ) , ( -5 , -320 ) , ( -8 , -200 ) , ( -10 , -160 ) , ( -16 , -100 ) , ( -20 , -80 ) , ( -25 , -64 ) , ( -32 , -50 ) and ( -40 , -40 ) .

#### 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. 1600 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1600.
• Every number is a factor of zero (0), since 1600 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, 160, 200, 320, 400, 800, 1600 are exact divisors of 1600.
• Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600. Each factor divides 1600 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, 160, 200, 320, 400, 800, 1600 are all less than or equal to 1600.

• Which is the smallest prime factor of 1600?

The smallest prime factor of 1600 is 2.

• Is 1600 a whole number?

Yes 1600 is a whole number.

• What are the prime factors of 1600?

The factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
Prime factors of 1600 are 2, 2, 2, 2, 2, 2, 5, 5.

• What two numbers make 1600?

Two numbers that make 1600 are 2 and 800.

• What are multiples of 1600?

First five multiples of 1600 are 3200, 4800, 6400, 8000.

• What is the sum of all factors of 1600?

The sum of all factors of 1600 is 3937.

• What are five multiples of 1600?

First five multiples of 1600 are 3200, 4800, 6400, 8000, 9600.

• Is 1600 a perfect square?

Yes 1600 is a perfect square.

• What is the greatest prime factors of 1600?

The greatest prime factor of 1600 is 5.

#### Examples of Factors

How many factors are there for 1600?

Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
So there are in total 21 factors.

Kevin has been asked to write 20 factor(s) of 1600. Can you predict the answer?

20 factor(s) of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800.

Sammy is puzzled while calculating the prime factors of 1600. Can you help him find them?

Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
Prime factors of 1600 are 2, 2, 2, 2, 2, 2, 5, 5

What is prime factorization of 1600?

Prime factorization of 1600 is 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 26 x 52.

Ariel has been assigned the task to find the product of all the prime factors of 1600. Can you help her?

Prime factors of 1600 are 2, 2, 2, 2, 2, 2, 5, 5.
Hence, the product of prime factors of 10.

Can you help Rubel to find out the product of the even factors of 1600?

Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
Even factors of 1600 are 2, 4, 8, 10, 16, 20, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
Hence, product of even factors of 1600 is; 2 x 4 x 8 x 10 x 16 x 20 x 32 x 40 x 50 x 64 x 80 x 100 x 160 x 200 x 320 x 400 x 800 x 1600 = 3.5184372088832e+31.

Joy wants to calculate mean of all the factors of 1600. Help him in finding the mean of 1600.

Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1600 is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 160 + 200 + 320 + 400 + 800 + 1600 = 3937.
Hence, the mean of factors of 1600 is 3937 ÷ 21 = 187.48.