# Factors of 2007

Factors of 2007 are 1, 3, 9, 223, 669, and 2007

#### How to find factors of a number

 1.   Find factors of 2007 using Division Method 2.   Find factors of 2007 using Prime Factorization 3.   Find factors of 2007 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2007

• Divide 2007 by 1: 2007 ÷ 1 : Remainder = 0
• Divide 2007 by 3: 2007 ÷ 3 : Remainder = 0
• Divide 2007 by 9: 2007 ÷ 9 : Remainder = 0
• Divide 2007 by 223: 2007 ÷ 223 : Remainder = 0
• Divide 2007 by 669: 2007 ÷ 669 : Remainder = 0
• Divide 2007 by 2007: 2007 ÷ 2007 : Remainder = 0

Hence, Factors of 2007 are 1, 3, 9, 223, 669, and 2007

#### 2. Steps to find factors of 2007 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 2007 using the division method, follow these steps:

• Step 1. Start dividing 2007 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 2007, which is 3. Divide 2007 by 3 to obtain the quotient (669).
2007 ÷ 3 = 669
• Step 3. Repeat step 1 with the obtained quotient (669).
669 ÷ 3 = 223
223 ÷ 223 = 1

So, the prime factorization of 2007 is, 2007 = 3 x 3 x 223.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2007 as shown below:

So, the prime factorization of 2007 is, 2007 = 3 x 3 x 223.

#### 3. Find factors of 2007 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 2007 would be the two numbers which, when multiplied, give 2007 as the result.

The following table represents the calculation of factors of 2007 in pairs:

Factor Pair Pair Factorization
1 and 2007 1 x 2007 = 2007
3 and 669 3 x 669 = 2007
9 and 223 9 x 223 = 2007

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 2007. They are called negative pair factors.

Hence, the negative pairs of 2007 would be ( -1 , -2007 ) , ( -3 , -669 ) and ( -9 , -223 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 2007 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, 3, 9, 223, 669, 2007 are exact divisors of 2007.
• Factors of 2007 are 1, 3, 9, 223, 669, 2007. Each factor divides 2007 without leaving a remainder.

• Which is the smallest prime factor of 2007?

Smallest prime factor of 2007 is 3.

• Is 2007 a perfect square?

No 2007 is not a perfect square.

• What are five multiples of 2007?

First five multiples of 2007 are 4014, 6021, 8028, 10035, 12042.

• What is prime factorization of 2007?

Prime factorization of 2007 is 3 x 3 x 223.

• What are factors of 2007?

Factors of 2007 are 1, 3, 9, 223, 669, 2007.

• How do you find factors of a negative number? ( eg. -2007 )?

Factors of -2007 are -1, -3, -9, -223, -669, -2007.

• Is 2007 a whole number?

Yes 2007 is a whole number.

• Which is greatest factor of 2007?

The greatest factor of 2007 is 669.

• What are the prime factors of 2007?

The factors of 2007 are 1, 3, 9, 223, 669, 2007.
Prime factors of 2007 are 3, 3, 223.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 2007. Can you help her?

Prime factors of 2007 are 3, 3, 223.
Hence, the product of prime factors of 669.

Can you help Rubel to find out the product of the even factors of 2007?

Factors of 2007 are 1, 3, 9, 223, 669, 2007.
Even factors of 2007 are 0.
Hence, product of even factors of 2007 is; 0 = 0.

Joy wants to calculate mean of all the factors of 2007. Help him in finding the mean of 2007.

Factors of 2007 are 1, 3, 9, 223, 669, 2007.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2007 is 1 + 3 + 9 + 223 + 669 + 2007 = 2912.
Hence, the mean of factors of 2007 is 2912 ÷ 6 = 485.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2007? Help her in writing all the factors.

Positive factors are 1, 3, 9, 223, 669, 2007.
Negative factors are -1, -3, -9, -223, -669, -2007.

How many factors are there for 2007?

Factors of 2007 are 1, 3, 9, 223, 669, 2007.
So there are in total 6 factors.

Joey wants to write all the prime factors of 2007 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2007 are 3, 3, 223.
So in exponential form it can be written as 32 x 223.

Kevin has been asked to write 5 factor(s) of 2007. Can you predict the answer?

5 factor(s) of 2007 are 1, 3, 9, 223, 669.