# Factors of 2205

Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, and 2205

#### How to find factors of a number

 1.   Find factors of 2205 using Division Method 2.   Find factors of 2205 using Prime Factorization 3.   Find factors of 2205 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2205

• Divide 2205 by 1: 2205 ÷ 1 : Remainder = 0
• Divide 2205 by 3: 2205 ÷ 3 : Remainder = 0
• Divide 2205 by 5: 2205 ÷ 5 : Remainder = 0
• Divide 2205 by 7: 2205 ÷ 7 : Remainder = 0
• Divide 2205 by 9: 2205 ÷ 9 : Remainder = 0
• Divide 2205 by 15: 2205 ÷ 15 : Remainder = 0
• Divide 2205 by 21: 2205 ÷ 21 : Remainder = 0
• Divide 2205 by 35: 2205 ÷ 35 : Remainder = 0
• Divide 2205 by 45: 2205 ÷ 45 : Remainder = 0
• Divide 2205 by 49: 2205 ÷ 49 : Remainder = 0
• Divide 2205 by 63: 2205 ÷ 63 : Remainder = 0
• Divide 2205 by 105: 2205 ÷ 105 : Remainder = 0
• Divide 2205 by 147: 2205 ÷ 147 : Remainder = 0
• Divide 2205 by 245: 2205 ÷ 245 : Remainder = 0
• Divide 2205 by 315: 2205 ÷ 315 : Remainder = 0
• Divide 2205 by 441: 2205 ÷ 441 : Remainder = 0
• Divide 2205 by 735: 2205 ÷ 735 : Remainder = 0
• Divide 2205 by 2205: 2205 ÷ 2205 : Remainder = 0

Hence, Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, and 2205

#### 2. Steps to find factors of 2205 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 2205 using the division method, follow these steps:

• Step 1. Start dividing 2205 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 2205, which is 3. Divide 2205 by 3 to obtain the quotient (735).
2205 ÷ 3 = 735
• Step 3. Repeat step 1 with the obtained quotient (735).
735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 2205 is, 2205 = 3 x 3 x 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2205 as shown below:

So, the prime factorization of 2205 is, 2205 = 3 x 3 x 5 x 7 x 7.

#### 3. Find factors of 2205 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 2205 would be the two numbers which, when multiplied, give 2205 as the result.

The following table represents the calculation of factors of 2205 in pairs:

Factor Pair Pair Factorization
1 and 2205 1 x 2205 = 2205
3 and 735 3 x 735 = 2205
5 and 441 5 x 441 = 2205
7 and 315 7 x 315 = 2205
9 and 245 9 x 245 = 2205
15 and 147 15 x 147 = 2205
21 and 105 21 x 105 = 2205
35 and 63 35 x 63 = 2205
45 and 49 45 x 49 = 2205

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 2205. They are called negative pair factors.

Hence, the negative pairs of 2205 would be ( -1 , -2205 ) , ( -3 , -735 ) , ( -5 , -441 ) , ( -7 , -315 ) , ( -9 , -245 ) , ( -15 , -147 ) , ( -21 , -105 ) , ( -35 , -63 ) and ( -45 , -49 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205 are exact divisors of 2205.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 2205 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2205.

• Which is the smallest prime factor of 2205?

Smallest prime factor of 2205 is 3.

• Is 2205 a perfect square?

No 2205 is not a perfect square.

• What are five multiples of 2205?

First five multiples of 2205 are 4410, 6615, 8820, 11025, 13230.

• What is prime factorization of 2205?

Prime factorization of 2205 is 3 x 3 x 5 x 7 x 7.

• What are factors of 2205?

Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.

• How do you find factors of a negative number? ( eg. -2205 )?

Factors of -2205 are -1, -3, -5, -7, -9, -15, -21, -35, -45, -49, -63, -105, -147, -245, -315, -441, -735, -2205.

• Is 2205 a whole number?

Yes 2205 is a whole number.

• Which is greatest factor of 2205?

The greatest factor of 2205 is 735.

• What are the prime factors of 2205?

The factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.
Prime factors of 2205 are 3, 3, 5, 7, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 2205. Can you help her?

Prime factors of 2205 are 3, 3, 5, 7, 7.
Hence, the product of prime factors of 105.

Can you help Rubel to find out the product of the even factors of 2205?

Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.
Even factors of 2205 are 0.
Hence, product of even factors of 2205 is; 0 = 0.

Joy wants to calculate mean of all the factors of 2205. Help him in finding the mean of 2205.

Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2205 is 1 + 3 + 5 + 7 + 9 + 15 + 21 + 35 + 45 + 49 + 63 + 105 + 147 + 245 + 315 + 441 + 735 + 2205 = 4446.
Hence, the mean of factors of 2205 is 4446 ÷ 18 = 247.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2205? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.
Negative factors are -1, -3, -5, -7, -9, -15, -21, -35, -45, -49, -63, -105, -147, -245, -315, -441, -735, -2205.

How many factors are there for 2205?

Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205.
So there are in total 18 factors.

Joey wants to write all the prime factors of 2205 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2205 are 3, 3, 5, 7, 7.
So in exponential form it can be written as 32 x 5 x 72.

Kevin has been asked to write 17 factor(s) of 2205. Can you predict the answer?

17 factor(s) of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735.