# Factors of 4000

Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, and 4000

#### How to find factors of a number

 1.   Find factors of 4000 using Division Method 2.   Find factors of 4000 using Prime Factorization 3.   Find factors of 4000 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 4000

• Divide 4000 by 1: 4000 ÷ 1 : Remainder = 0
• Divide 4000 by 2: 4000 ÷ 2 : Remainder = 0
• Divide 4000 by 4: 4000 ÷ 4 : Remainder = 0
• Divide 4000 by 5: 4000 ÷ 5 : Remainder = 0
• Divide 4000 by 8: 4000 ÷ 8 : Remainder = 0
• Divide 4000 by 10: 4000 ÷ 10 : Remainder = 0
• Divide 4000 by 16: 4000 ÷ 16 : Remainder = 0
• Divide 4000 by 20: 4000 ÷ 20 : Remainder = 0
• Divide 4000 by 25: 4000 ÷ 25 : Remainder = 0
• Divide 4000 by 32: 4000 ÷ 32 : Remainder = 0
• Divide 4000 by 40: 4000 ÷ 40 : Remainder = 0
• Divide 4000 by 50: 4000 ÷ 50 : Remainder = 0
• Divide 4000 by 80: 4000 ÷ 80 : Remainder = 0
• Divide 4000 by 100: 4000 ÷ 100 : Remainder = 0
• Divide 4000 by 125: 4000 ÷ 125 : Remainder = 0
• Divide 4000 by 160: 4000 ÷ 160 : Remainder = 0
• Divide 4000 by 200: 4000 ÷ 200 : Remainder = 0
• Divide 4000 by 250: 4000 ÷ 250 : Remainder = 0
• Divide 4000 by 400: 4000 ÷ 400 : Remainder = 0
• Divide 4000 by 500: 4000 ÷ 500 : Remainder = 0
• Divide 4000 by 800: 4000 ÷ 800 : Remainder = 0
• Divide 4000 by 1000: 4000 ÷ 1000 : Remainder = 0
• Divide 4000 by 2000: 4000 ÷ 2000 : Remainder = 0
• Divide 4000 by 4000: 4000 ÷ 4000 : Remainder = 0

Hence, Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, and 4000

#### 2. Steps to find factors of 4000 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 4000 using the division method, follow these steps:

• Step 1. Start dividing 4000 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 4000, which is 2. Divide 4000 by 2 to obtain the quotient (2000).
4000 ÷ 2 = 2000
• Step 3. Repeat step 1 with the obtained quotient (2000).
2000 ÷ 2 = 1000
1000 ÷ 2 = 500
500 ÷ 2 = 250
250 ÷ 2 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 4000 is, 4000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 4000 as shown below:

So, the prime factorization of 4000 is, 4000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5.

#### 3. Find factors of 4000 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 4000 would be the two numbers which, when multiplied, give 4000 as the result.

The following table represents the calculation of factors of 4000 in pairs:

Factor Pair Pair Factorization
1 and 4000 1 x 4000 = 4000
2 and 2000 2 x 2000 = 4000
4 and 1000 4 x 1000 = 4000
5 and 800 5 x 800 = 4000
8 and 500 8 x 500 = 4000
10 and 400 10 x 400 = 4000
16 and 250 16 x 250 = 4000
20 and 200 20 x 200 = 4000
25 and 160 25 x 160 = 4000
32 and 125 32 x 125 = 4000
40 and 100 40 x 100 = 4000
50 and 80 50 x 80 = 4000

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 4000. They are called negative pair factors.

Hence, the negative pairs of 4000 would be ( -1 , -4000 ) , ( -2 , -2000 ) , ( -4 , -1000 ) , ( -5 , -800 ) , ( -8 , -500 ) , ( -10 , -400 ) , ( -16 , -250 ) , ( -20 , -200 ) , ( -25 , -160 ) , ( -32 , -125 ) , ( -40 , -100 ) and ( -50 , -80 ) .

#### 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. 4000 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 4000.
• Every number is a factor of zero (0), since 4000 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, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 are exact divisors of 4000.
• Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000. Each factor divides 4000 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, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 are all less than or equal to 4000.

• Is 4000 a perfect square?

No 4000 is not a perfect square.

• What are factors of 4000?

Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.

• Which is greatest factor of 4000?

The greatest factor of 4000 is 2000.

• What is the sum of all factors of 4000?

The sum of all factors of 4000 is 9828.

• What are multiples of 4000?

First five multiples of 4000 are 8000, 12000, 16000, 20000.

• What is the greatest prime factors of 4000?

The greatest prime factor of 4000 is 5.

• What are six multiples of 4000?

First five multiples of 4000 are 8000, 12000, 16000, 20000, 24000, 28000.

• What is prime factorization of 4000?

Prime factorization of 4000 is 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5.

• Is 4000 a whole number?

Yes 4000 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 4000? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -125, -160, -200, -250, -400, -500, -800, -1000, -2000, -4000.

Can you help Sammy find out the product of the odd factors of 4000?

Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.
Odd factors of 4000 are 1, 5, 25, 125.
Hence product of odd factors of 4000 is; 1 x 5 x 25 x 125 = 15625.

Joey wants to write all the prime factors of 4000 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 4000 are 2, 2, 2, 2, 2, 5, 5, 5.
So in exponential form it can be written as 25 x 53.

How many factors are there for 4000?

Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 4000. Can you predict the answer?

23 factor(s) of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000.

Sammy is puzzled while calculating the prime factors of 4000. Can you help him find them?

Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.
Prime factors of 4000 are 2, 2, 2, 2, 2, 5, 5, 5

What is prime factorization of 4000?

Prime factorization of 4000 is 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 = 25 x 53.