# Factors of 208

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208

#### How to find factors of a number

 1.   Find factors of 208 using Division Method 2.   Find factors of 208 using Prime Factorization 3.   Find factors of 208 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 208

• Divide 208 by 1: 208 ÷ 1 : Remainder = 0
• Divide 208 by 2: 208 ÷ 2 : Remainder = 0
• Divide 208 by 4: 208 ÷ 4 : Remainder = 0
• Divide 208 by 8: 208 ÷ 8 : Remainder = 0
• Divide 208 by 13: 208 ÷ 13 : Remainder = 0
• Divide 208 by 16: 208 ÷ 16 : Remainder = 0
• Divide 208 by 26: 208 ÷ 26 : Remainder = 0
• Divide 208 by 52: 208 ÷ 52 : Remainder = 0
• Divide 208 by 104: 208 ÷ 104 : Remainder = 0
• Divide 208 by 208: 208 ÷ 208 : Remainder = 0

Hence, Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208

#### 2. Steps to find factors of 208 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 208 using the division method, follow these steps:

• Step 1. Start dividing 208 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 208, which is 2. Divide 208 by 2 to obtain the quotient (104).
208 ÷ 2 = 104
• Step 3. Repeat step 1 with the obtained quotient (104).
104 ÷ 2 = 52
52 ÷ 2 = 26
26 ÷ 2 = 13
13 ÷ 13 = 1

So, the prime factorization of 208 is, 208 = 2 x 2 x 2 x 2 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 208 as shown below:

So, the prime factorization of 208 is, 208 = 2 x 2 x 2 x 2 x 13.

#### 3. Find factors of 208 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 208 would be the two numbers which, when multiplied, give 208 as the result.

The following table represents the calculation of factors of 208 in pairs:

Factor Pair Pair Factorization
1 and 208 1 x 208 = 208
2 and 104 2 x 104 = 208
4 and 52 4 x 52 = 208
8 and 26 8 x 26 = 208
13 and 16 13 x 16 = 208

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 208. They are called negative pair factors.

Hence, the negative pairs of 208 would be ( -1 , -208 ) , ( -2 , -104 ) , ( -4 , -52 ) , ( -8 , -26 ) and ( -13 , -16 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 208 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 208.
• Every number is a factor of zero (0), since 208 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, 2, 4, 8, 13, 16, 26, 52, 104, 208 are exact divisors of 208.
• Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. Each factor divides 208 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 are all less than or equal to 208.

• What are the prime factors of 208?

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Prime factors of 208 are 2, 2, 2, 2, 13.

• What is the sum of all factors of 208?

The sum of all factors of 208 is 434.

• What are the pair factors of 208?

Pair factors of 208 are (1,208), (2,104), (4,52), (8,26), (13,16).

• What two numbers make 208?

Two numbers that make 208 are 2 and 104.

• What are multiples of 208?

First five multiples of 208 are 416, 624, 832, 1040.

• Is 208 a perfect square?

No 208 is not a perfect square.

• Which is greatest factor of 208?

The greatest factor of 208 is 104.

• How do you factors of 208?

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.

• What are five multiples of 208?

First five multiples of 208 are 416, 624, 832, 1040, 1248.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 208?

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Even factors of 208 are 2, 4, 8, 16, 26, 52, 104, 208.
Hence, product of even factors of 208 is; 2 x 4 x 8 x 16 x 26 x 52 x 104 x 208 = 29948379136.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 208? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Negative factors are -1, -2, -4, -8, -13, -16, -26, -52, -104, -208.

How many factors are there for 208?

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
So there are in total 10 factors.

Sammy is puzzled while calculating the prime factors of 208. Can you help him find them?

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Prime factors of 208 are 2, 2, 2, 2, 13

Joey wants to write all the prime factors of 208 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 208 are 2, 2, 2, 2, 13.
So in exponential form it can be written as 24 x 13.

What is prime factorization of 208?

Prime factorization of 208 is 2 x 2 x 2 x 2 x 13 = 24 x 13.

Can you help Rubel to find out the product of the even factors of 208?

Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.
Even factors of 208 are 2, 4, 8, 16, 26, 52, 104, 208.
Hence, product of even factors of 208 is; 2 x 4 x 8 x 16 x 26 x 52 x 104 x 208 = 29948379136.