# Factors of 2004

Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, and 2004

#### How to find factors of a number

 1.   Find factors of 2004 using Division Method 2.   Find factors of 2004 using Prime Factorization 3.   Find factors of 2004 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2004

• Divide 2004 by 1: 2004 ÷ 1 : Remainder = 0
• Divide 2004 by 2: 2004 ÷ 2 : Remainder = 0
• Divide 2004 by 3: 2004 ÷ 3 : Remainder = 0
• Divide 2004 by 4: 2004 ÷ 4 : Remainder = 0
• Divide 2004 by 6: 2004 ÷ 6 : Remainder = 0
• Divide 2004 by 12: 2004 ÷ 12 : Remainder = 0
• Divide 2004 by 167: 2004 ÷ 167 : Remainder = 0
• Divide 2004 by 334: 2004 ÷ 334 : Remainder = 0
• Divide 2004 by 501: 2004 ÷ 501 : Remainder = 0
• Divide 2004 by 668: 2004 ÷ 668 : Remainder = 0
• Divide 2004 by 1002: 2004 ÷ 1002 : Remainder = 0
• Divide 2004 by 2004: 2004 ÷ 2004 : Remainder = 0

Hence, Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, and 2004

#### 2. Steps to find factors of 2004 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 2004 using the division method, follow these steps:

• Step 1. Start dividing 2004 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 2004, which is 2. Divide 2004 by 2 to obtain the quotient (1002).
2004 ÷ 2 = 1002
• Step 3. Repeat step 1 with the obtained quotient (1002).
1002 ÷ 2 = 501
501 ÷ 3 = 167
167 ÷ 167 = 1

So, the prime factorization of 2004 is, 2004 = 2 x 2 x 3 x 167.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2004 as shown below:

So, the prime factorization of 2004 is, 2004 = 2 x 2 x 3 x 167.

#### 3. Find factors of 2004 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 2004 would be the two numbers which, when multiplied, give 2004 as the result.

The following table represents the calculation of factors of 2004 in pairs:

Factor Pair Pair Factorization
1 and 2004 1 x 2004 = 2004
2 and 1002 2 x 1002 = 2004
3 and 668 3 x 668 = 2004
4 and 501 4 x 501 = 2004
6 and 334 6 x 334 = 2004
12 and 167 12 x 167 = 2004

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 2004. They are called negative pair factors.

Hence, the negative pairs of 2004 would be ( -1 , -2004 ) , ( -2 , -1002 ) , ( -3 , -668 ) , ( -4 , -501 ) , ( -6 , -334 ) and ( -12 , -167 ) .

#### How can we define factors?

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

#### Properties of factors

• Each number is a factor of itself. Eg. 2004 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2004.
• Every number is a factor of zero (0), since 2004 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, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004 are exact divisors of 2004.
• Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004. Each factor divides 2004 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004 are all less than or equal to 2004.

• How do you find factors of a negative number? ( eg. -2004 )?

Factors of -2004 are -1, -2, -3, -4, -6, -12, -167, -334, -501, -668, -1002, -2004.

• What is the sum of all factors of 2004?

The sum of all factors of 2004 is 4704.

• What is prime factorization of 2004?

Prime factorization of 2004 is 2 x 2 x 3 x 167.

• What are the pair factors of 2004?

Pair factors of 2004 are (1,2004), (2,1002), (3,668), (4,501), (6,334), (12,167).

• What are six multiples of 2004?

First five multiples of 2004 are 4008, 6012, 8016, 10020, 12024, 14028.

• Is 2004 a whole number?

Yes 2004 is a whole number.

• Which is the smallest prime factor of 2004?

Smallest prime factor of 2004 is 2.

• What are five multiples of 2004?

First five multiples of 2004 are 4008, 6012, 8016, 10020, 12024.

• Write all factors of 2004?

Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.

#### Examples of Factors

Joey wants to write all the prime factors of 2004 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2004 are 2, 2, 3, 167.
So in exponential form it can be written as 22 x 3 x 167.

How many factors are there for 2004?

Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 2004. Can you predict the answer?

11 factor(s) of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002.

Sammy is puzzled while calculating the prime factors of 2004. Can you help him find them?

Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.
Prime factors of 2004 are 2, 2, 3, 167

What is prime factorization of 2004?

Prime factorization of 2004 is 2 x 2 x 3 x 167 = 22 x 3 x 167.

Ariel has been assigned the task to find the product of all the prime factors of 2004. Can you help her?

Prime factors of 2004 are 2, 2, 3, 167.
Hence, the product of prime factors of 1002.

Can you help Rubel to find out the product of the even factors of 2004?

Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.
Even factors of 2004 are 2, 4, 6, 12, 334, 668, 1002, 2004.
Hence, product of even factors of 2004 is; 2 x 4 x 6 x 12 x 334 x 668 x 1002 x 2004 = 258054152196096.