1. Steps to find factors of 2009 using Division Method

Example: Find factors of 2009

  • Divide 2009 by 1: 2009 ÷ 1 : Remainder = 0
  • Divide 2009 by 7: 2009 ÷ 7 : Remainder = 0
  • Divide 2009 by 41: 2009 ÷ 41 : Remainder = 0
  • Divide 2009 by 49: 2009 ÷ 49 : Remainder = 0
  • Divide 2009 by 287: 2009 ÷ 287 : Remainder = 0
  • Divide 2009 by 2009: 2009 ÷ 2009 : Remainder = 0

Hence, Factors of 2009 are 1, 7, 41, 49, 287, and 2009

2. Steps to find factors of 2009 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 2009 using the division method, follow these steps:

  • Step 1. Start dividing 2009 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 2009, which is 7. Divide 2009 by 7 to obtain the quotient (287).
    2009 ÷ 7 = 287
  • Step 3. Repeat step 1 with the obtained quotient (287).
    287 ÷ 7 = 41
    41 ÷ 41 = 1

So, the prime factorization of 2009 is, 2009 = 7 x 7 x 41.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2009 as shown below:

So, the prime factorization of 2009 is, 2009 = 7 x 7 x 41.

3. Find factors of 2009 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 2009 would be the two numbers which, when multiplied, give 2009 as the result.

The following table represents the calculation of factors of 2009 in pairs:

Factor Pair Pair Factorization
1 and 2009 1 x 2009 = 2009
7 and 287 7 x 287 = 2009
41 and 49 41 x 49 = 2009

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 2009. They are called negative pair factors.

Hence, the negative pairs of 2009 would be ( -1 , -2009 ) , ( -7 , -287 ) and ( -41 , -49 ) .

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

  • Every factor of a number is an exact divisor of that number, example 1, 7, 41, 49, 287, 2009 are exact divisors of 2009.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 2009 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2009.

Frequently Asked Questions

  • What two numbers make 2009?

    Two numbers that make 2009 are 7 and 287.

  • What is prime factorization of 2009?

    Prime factorization of 2009 is 7 x 7 x 41.

  • Write some multiples of 2009?

    First five multiples of 2009 are 4018, 6027, 8036, 10045.

  • Which is the smallest prime factor of 2009?

    The smallest prime factor of 2009 is 7.

  • Is 2009 a perfect square?

    No 2009 is not a perfect square.

  • What is the sum of all factors of 2009?

    The sum of all factors of 2009 is 2394.

  • What are factors of 2009?

    Factors of 2009 are 1, 7, 41, 49, 287, 2009.

  • How do you find factors of a negative number? ( eg. -2009 )?

    Factors of -2009 are -1, -7, -41, -49, -287, -2009.

  • Is 2009 a whole number?

    Yes 2009 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 2009. Help him in finding the mean of 2009.

Factors of 2009 are 1, 7, 41, 49, 287, 2009.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2009 is 1 + 7 + 41 + 49 + 287 + 2009 = 2394.
Hence, the mean of factors of 2009 is 2394 ÷ 6 = 399.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2009? Help her in writing all the factors.

Positive factors are 1, 7, 41, 49, 287, 2009.
Negative factors are -1, -7, -41, -49, -287, -2009.

Joey wants to write all the prime factors of 2009 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2009 are 7, 7, 41.
So in exponential form it can be written as 72 x 41.

Kevin has been asked to write 5 factor(s) of 2009. Can you predict the answer?

5 factor(s) of 2009 are 1, 7, 41, 49, 287.

Sammy is puzzled while calculating the prime factors of 2009. Can you help him find them?

Factors of 2009 are 1, 7, 41, 49, 287, 2009.
Prime factors of 2009 are 7, 7, 41

What is prime factorization of 2009?

Prime factorization of 2009 is 7 x 7 x 41 = 72 x 41.

Can you help Rubel to find out the product of the even factors of 2009?

Factors of 2009 are 1, 7, 41, 49, 287, 2009.
Even factors of 2009 are 0.
Hence, product of even factors of 2009 is; 0 = 0.