# Factors of 2005

Factors of 2005 are 1, 5, 401, and 2005

#### How to find factors of a number

 1.   Find factors of 2005 using Division Method 2.   Find factors of 2005 using Prime Factorization 3.   Find factors of 2005 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2005

• Divide 2005 by 1: 2005 ÷ 1 : Remainder = 0
• Divide 2005 by 5: 2005 ÷ 5 : Remainder = 0
• Divide 2005 by 401: 2005 ÷ 401 : Remainder = 0
• Divide 2005 by 2005: 2005 ÷ 2005 : Remainder = 0

Hence, Factors of 2005 are 1, 5, 401, and 2005

#### 2. Steps to find factors of 2005 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 2005 using the division method, follow these steps:

• Step 1. Start dividing 2005 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 2005, which is 5. Divide 2005 by 5 to obtain the quotient (401).
2005 ÷ 5 = 401
• Step 3. Repeat step 1 with the obtained quotient (401).
401 ÷ 401 = 1

So, the prime factorization of 2005 is, 2005 = 5 x 401.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2005 as shown below:

So, the prime factorization of 2005 is, 2005 = 5 x 401.

#### 3. Find factors of 2005 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 2005 would be the two numbers which, when multiplied, give 2005 as the result.

The following table represents the calculation of factors of 2005 in pairs:

Factor Pair Pair Factorization
1 and 2005 1 x 2005 = 2005
5 and 401 5 x 401 = 2005

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 2005. They are called negative pair factors.

Hence, the negative pairs of 2005 would be ( -1 , -2005 ) , ( -5 , -401 ) .

#### 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, 5, 401, 2005 are exact divisors of 2005.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 2005 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2005.

• Which is the smallest prime factor of 2005?

The smallest prime factor of 2005 is 5.

• Is 2005 a whole number?

Yes 2005 is a whole number.

• What are the prime factors of 2005?

The factors of 2005 are 1, 5, 401, 2005.
Prime factors of 2005 are 5, 401.

• What two numbers make 2005?

Two numbers that make 2005 are 5 and 401.

• What are multiples of 2005?

First five multiples of 2005 are 4010, 6015, 8020, 10025.

• What is the sum of all factors of 2005?

The sum of all factors of 2005 is 2412.

• What are five multiples of 2005?

First five multiples of 2005 are 4010, 6015, 8020, 10025, 12030.

• Is 2005 a perfect square?

No 2005 is not a perfect square.

• What is the greatest prime factors of 2005?

The greatest prime factor of 2005 is 401.

#### Examples of Factors

How many factors are there for 2005?

Factors of 2005 are 1, 5, 401, 2005.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 2005. Can you predict the answer?

3 factor(s) of 2005 are 1, 5, 401.

Sammy is puzzled while calculating the prime factors of 2005. Can you help him find them?

Factors of 2005 are 1, 5, 401, 2005.
Prime factors of 2005 are 5, 401

What is prime factorization of 2005?

Prime factorization of 2005 is 5 x 401 = 5 x 401.

Ariel has been assigned the task to find the product of all the prime factors of 2005. Can you help her?

Prime factors of 2005 are 5, 401.
Hence, the product of prime factors of 2005.

Can you help Rubel to find out the product of the even factors of 2005?

Factors of 2005 are 1, 5, 401, 2005.
Even factors of 2005 are 0.
Hence, product of even factors of 2005 is; 0 = 0.

Joy wants to calculate mean of all the factors of 2005. Help him in finding the mean of 2005.

Factors of 2005 are 1, 5, 401, 2005.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2005 is 1 + 5 + 401 + 2005 = 2412.
Hence, the mean of factors of 2005 is 2412 ÷ 4 = 603.00.