# Factors of 209

Factors of 209 are 1, 11, 19, and 209

#### How to find factors of a number

 1.   Find factors of 209 using Division Method 2.   Find factors of 209 using Prime Factorization 3.   Find factors of 209 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 209

• Divide 209 by 1: 209 ÷ 1 : Remainder = 0
• Divide 209 by 11: 209 ÷ 11 : Remainder = 0
• Divide 209 by 19: 209 ÷ 19 : Remainder = 0
• Divide 209 by 209: 209 ÷ 209 : Remainder = 0

Hence, Factors of 209 are 1, 11, 19, and 209

#### 2. Steps to find factors of 209 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 209 using the division method, follow these steps:

• Step 1. Start dividing 209 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 209, which is 11. Divide 209 by 11 to obtain the quotient (19).
209 ÷ 11 = 19
• Step 3. Repeat step 1 with the obtained quotient (19).
19 ÷ 19 = 1

So, the prime factorization of 209 is, 209 = 11 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 209 as shown below:

So, the prime factorization of 209 is, 209 = 11 x 19.

#### 3. Find factors of 209 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 209 would be the two numbers which, when multiplied, give 209 as the result.

The following table represents the calculation of factors of 209 in pairs:

Factor Pair Pair Factorization
1 and 209 1 x 209 = 209
11 and 19 11 x 19 = 209

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 209. They are called negative pair factors.

Hence, the negative pairs of 209 would be ( -1 , -209 ) , ( -11 , -19 ) .

#### 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, 11, 19, 209 are exact divisors of 209.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 209 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 209.

• What two numbers make 209?

Two numbers that make 209 are 11 and 19.

• What is prime factorization of 209?

Prime factorization of 209 is 11 x 19.

• Write some multiples of 209?

First five multiples of 209 are 418, 627, 836, 1045.

• Which is the smallest prime factor of 209?

The smallest prime factor of 209 is 11.

• Is 209 a perfect square?

No 209 is not a perfect square.

• What is the sum of all factors of 209?

The sum of all factors of 209 is 240.

• What are factors of 209?

Factors of 209 are 1, 11, 19, 209.

• How do you find factors of a negative number? ( eg. -209 )?

Factors of -209 are -1, -11, -19, -209.

• Is 209 a whole number?

Yes 209 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 209. Help him in finding the mean of 209.

Factors of 209 are 1, 11, 19, 209.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 209 is 1 + 11 + 19 + 209 = 240.
Hence, the mean of factors of 209 is 240 ÷ 4 = 60.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 209? Help her in writing all the factors.

Positive factors are 1, 11, 19, 209.
Negative factors are -1, -11, -19, -209.

Joey wants to write all the prime factors of 209 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 209 are 11, 19.
So in exponential form it can be written as 11 x 19.

Kevin has been asked to write 3 factor(s) of 209. Can you predict the answer?

3 factor(s) of 209 are 1, 11, 19.

Sammy is puzzled while calculating the prime factors of 209. Can you help him find them?

Factors of 209 are 1, 11, 19, 209.
Prime factors of 209 are 11, 19

What is prime factorization of 209?

Prime factorization of 209 is 11 x 19 = 11 x 19.

Can you help Rubel to find out the product of the even factors of 209?

Factors of 209 are 1, 11, 19, 209.
Even factors of 209 are 0.
Hence, product of even factors of 209 is; 0 = 0.