# Factors of 209 in pair

Factors of 209 in pair are (1, 209) , (11, 19)

#### How to find factors of a number in pair

 1.   Steps to find factors of 209 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 209 in pair

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 ) .

#### What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- Factors of 209 are 1 , 11 , 19 , 209. So, factors of 209 in pair are (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.

#### Steps to find Factors of 209

• Step 1. Find all the numbers that would divide 209 without leaving any remainder. Starting with the number 1 upto 104 (half of 209). The number 1 and the number itself are always factors of the given number.
209 ÷ 1 : Remainder = 0
209 ÷ 11 : Remainder = 0
209 ÷ 19 : Remainder = 0
209 ÷ 209 : Remainder = 0

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

• Is 209 a perfect square?

No 209 is not a perfect square.

• Write five multiples of 209.

Five multiples of 209 are 418, 627, 836, 1045, 1254.

• Is there any even prime factor of 209?

No there is no even prime factor, i.e. 2, of 209.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Can you help Rubel in arranging 209 blocks in order to form a rectangle in all possible ways? For arranging 209 blocks in order to form a rectangle in all possible ways we need to find factors of 209 in pair.

Factors of 209 are 1, 11, 19, 209. So, factors of 209 in pair are (1,209), (11,19).

How many total number of factors of 209 in pair are possible?

Factors of 209 are 1, 11, 19, 209. Hence, the factors of 209 in pair are (1,209), (11,19). Therefore, in total 2 pairs of factors are possible.

Sammy wants to write all the negative factors of 209 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 209 are -1, -11, -19, -209. Hence, factors of 209 in pair are (-1,-209), (-11,-19).

Find the product of all prime factors of 209.

Factors of 209 are 1, 11, 19, 209. Prime factors are 11, 19. So, the product of all prime factors of 209 would be 11 x 19 = 209.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 209.
- Writing all prime factors of 209.
- Writing all the possible factors of 209 in pair.
Help him in writing all these.

Positive factors of 209 are 1, 11, 19, 209.
Prime factors of 209 are 11, 19.
Factors of 209 in pair are (1,209), (11,19).

Can you help Sammy list the factors of 209 and also find the factor pairs?

Factors of 209 are 1, 11, 19, 209.
Factors of 209 in pair are (1,209), (11,19).

Help Diji in finding factors of 209 by Prime Factorization method and then sorting factors of 209 in pairs.

Prime factorization of 209 is 11 x 19. Factors of 209 in pair can be written as (1,209), (11,19).

Write the smallest prime factor of 209.

Smallest prime factor of 209 is 11.