# Factors of 204

Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204

#### How to find factors of a number

 1.   Find factors of 204 using Division Method 2.   Find factors of 204 using Prime Factorization 3.   Find factors of 204 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 204

• Divide 204 by 1: 204 ÷ 1 : Remainder = 0
• Divide 204 by 2: 204 ÷ 2 : Remainder = 0
• Divide 204 by 3: 204 ÷ 3 : Remainder = 0
• Divide 204 by 4: 204 ÷ 4 : Remainder = 0
• Divide 204 by 6: 204 ÷ 6 : Remainder = 0
• Divide 204 by 12: 204 ÷ 12 : Remainder = 0
• Divide 204 by 17: 204 ÷ 17 : Remainder = 0
• Divide 204 by 34: 204 ÷ 34 : Remainder = 0
• Divide 204 by 51: 204 ÷ 51 : Remainder = 0
• Divide 204 by 68: 204 ÷ 68 : Remainder = 0
• Divide 204 by 102: 204 ÷ 102 : Remainder = 0
• Divide 204 by 204: 204 ÷ 204 : Remainder = 0

Hence, Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204

#### 2. Steps to find factors of 204 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 204 using the division method, follow these steps:

• Step 1. Start dividing 204 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 204, which is 2. Divide 204 by 2 to obtain the quotient (102).
204 ÷ 2 = 102
• Step 3. Repeat step 1 with the obtained quotient (102).
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1

So, the prime factorization of 204 is, 204 = 2 x 2 x 3 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 204 as shown below:

So, the prime factorization of 204 is, 204 = 2 x 2 x 3 x 17.

#### 3. Find factors of 204 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 204 would be the two numbers which, when multiplied, give 204 as the result.

The following table represents the calculation of factors of 204 in pairs:

Factor Pair Pair Factorization
1 and 204 1 x 204 = 204
2 and 102 2 x 102 = 204
3 and 68 3 x 68 = 204
4 and 51 4 x 51 = 204
6 and 34 6 x 34 = 204
12 and 17 12 x 17 = 204

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 204. They are called negative pair factors.

Hence, the negative pairs of 204 would be ( -1 , -204 ) , ( -2 , -102 ) , ( -3 , -68 ) , ( -4 , -51 ) , ( -6 , -34 ) and ( -12 , -17 ) .

#### 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. 204 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 204.
• Every number is a factor of zero (0), since 204 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, 17, 34, 51, 68, 102, 204 are exact divisors of 204.
• Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. Each factor divides 204 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204 are all less than or equal to 204.

• How do you find factors of a negative number? ( eg. -204 )?

Factors of -204 are -1, -2, -3, -4, -6, -12, -17, -34, -51, -68, -102, -204.

• What is the sum of all factors of 204?

The sum of all factors of 204 is 504.

• What is prime factorization of 204?

Prime factorization of 204 is 2 x 2 x 3 x 17.

• What are the pair factors of 204?

Pair factors of 204 are (1,204), (2,102), (3,68), (4,51), (6,34), (12,17).

• What are six multiples of 204?

First five multiples of 204 are 408, 612, 816, 1020, 1224, 1428.

• Is 204 a whole number?

Yes 204 is a whole number.

• Which is the smallest prime factor of 204?

Smallest prime factor of 204 is 2.

• What are five multiples of 204?

First five multiples of 204 are 408, 612, 816, 1020, 1224.

• Write all factors of 204?

Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.

#### Examples of Factors

Joey wants to write all the prime factors of 204 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 204 are 2, 2, 3, 17.
So in exponential form it can be written as 22 x 3 x 17.

How many factors are there for 204?

Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 204. Can you predict the answer?

11 factor(s) of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102.

Sammy is puzzled while calculating the prime factors of 204. Can you help him find them?

Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
Prime factors of 204 are 2, 2, 3, 17

What is prime factorization of 204?

Prime factorization of 204 is 2 x 2 x 3 x 17 = 22 x 3 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 204. Can you help her?

Prime factors of 204 are 2, 2, 3, 17.
Hence, the product of prime factors of 102.

Can you help Rubel to find out the product of the even factors of 204?

Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
Even factors of 204 are 2, 4, 6, 12, 34, 68, 102, 204.
Hence, product of even factors of 204 is; 2 x 4 x 6 x 12 x 34 x 68 x 102 x 204 = 27710263296.