1. Steps to find factors of 2209 using Division Method

Example: Find factors of 2209

  • Divide 2209 by 1: 2209 ÷ 1 : Remainder = 0
  • Divide 2209 by 47: 2209 ÷ 47 : Remainder = 0
  • Divide 2209 by 2209: 2209 ÷ 2209 : Remainder = 0

Hence, Factors of 2209 are 1, 47, and 2209

2. Steps to find factors of 2209 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 2209 using the division method, follow these steps:

  • Step 1. Start dividing 2209 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 2209, which is 47. Divide 2209 by 47 to obtain the quotient (47).
    2209 ÷ 47 = 47
  • Step 3. Repeat step 1 with the obtained quotient (47).
    47 ÷ 47 = 1

So, the prime factorization of 2209 is, 2209 = 47 x 47.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2209 as shown below:

So, the prime factorization of 2209 is, 2209 = 47 x 47.

3. Find factors of 2209 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 2209 would be the two numbers which, when multiplied, give 2209 as the result.

The following table represents the calculation of factors of 2209 in pairs:

Factor Pair Pair Factorization
1 and 2209 1 x 2209 = 2209
47 and 47 47 x 47 = 2209

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 2209. They are called negative pair factors.

Hence, the negative pairs of 2209 would be ( -1 , -2209 ) , ( -47 , -47 ) .

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, 47, 2209 are exact divisors of 2209.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 2209 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2209.

Frequently Asked Questions

  • Is 2209 a perfect square?

    Yes 2209 is a perfect square.

  • What are factors of 2209?

    Factors of 2209 are 1, 47, 2209.

  • Which is greatest factor of 2209?

    The greatest factor of 2209 is 47.

  • What is the sum of all factors of 2209?

    The sum of all factors of 2209 is 2257.

  • What are multiples of 2209?

    First five multiples of 2209 are 4418, 6627, 8836, 11045.

  • What is the greatest prime factors of 2209?

    The greatest prime factor of 2209 is 47.

  • What are six multiples of 2209?

    First five multiples of 2209 are 4418, 6627, 8836, 11045, 13254, 15463.

  • What is prime factorization of 2209?

    Prime factorization of 2209 is 47 x 47.

  • Is 2209 a whole number?

    Yes 2209 is a whole number.

Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2209? Help her in writing all the factors.

Positive factors are 1, 47, 2209.
Negative factors are -1, -47, -2209.

Can you help Sammy find out the product of the odd factors of 2209?

Factors of 2209 are 1, 47, 2209.
Odd factors of 2209 are 1, 47, 2209.
Hence product of odd factors of 2209 is; 1 x 47 x 2209 = 103823.

Joey wants to write all the prime factors of 2209 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2209 are 47, 47.
So in exponential form it can be written as 472.

How many factors are there for 2209?

Factors of 2209 are 1, 47, 2209.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 2209. Can you predict the answer?

2 factor(s) of 2209 are 1, 47.

Sammy is puzzled while calculating the prime factors of 2209. Can you help him find them?

Factors of 2209 are 1, 47, 2209.
Prime factors of 2209 are 47, 47

What is prime factorization of 2209?

Prime factorization of 2209 is 47 x 47 = 472.