# Factors of 308

Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, and 308

#### How to find factors of a number

 1.   Find factors of 308 using Division Method 2.   Find factors of 308 using Prime Factorization 3.   Find factors of 308 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 308

• Divide 308 by 1: 308 ÷ 1 : Remainder = 0
• Divide 308 by 2: 308 ÷ 2 : Remainder = 0
• Divide 308 by 4: 308 ÷ 4 : Remainder = 0
• Divide 308 by 7: 308 ÷ 7 : Remainder = 0
• Divide 308 by 11: 308 ÷ 11 : Remainder = 0
• Divide 308 by 14: 308 ÷ 14 : Remainder = 0
• Divide 308 by 22: 308 ÷ 22 : Remainder = 0
• Divide 308 by 28: 308 ÷ 28 : Remainder = 0
• Divide 308 by 44: 308 ÷ 44 : Remainder = 0
• Divide 308 by 77: 308 ÷ 77 : Remainder = 0
• Divide 308 by 154: 308 ÷ 154 : Remainder = 0
• Divide 308 by 308: 308 ÷ 308 : Remainder = 0

Hence, Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, and 308

#### 2. Steps to find factors of 308 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 308 using the division method, follow these steps:

• Step 1. Start dividing 308 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 308, which is 2. Divide 308 by 2 to obtain the quotient (154).
308 ÷ 2 = 154
• Step 3. Repeat step 1 with the obtained quotient (154).
154 ÷ 2 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 308 is, 308 = 2 x 2 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 308 as shown below:

So, the prime factorization of 308 is, 308 = 2 x 2 x 7 x 11.

#### 3. Find factors of 308 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 308 would be the two numbers which, when multiplied, give 308 as the result.

The following table represents the calculation of factors of 308 in pairs:

Factor Pair Pair Factorization
1 and 308 1 x 308 = 308
2 and 154 2 x 154 = 308
4 and 77 4 x 77 = 308
7 and 44 7 x 44 = 308
11 and 28 11 x 28 = 308
14 and 22 14 x 22 = 308

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 308. They are called negative pair factors.

Hence, the negative pairs of 308 would be ( -1 , -308 ) , ( -2 , -154 ) , ( -4 , -77 ) , ( -7 , -44 ) , ( -11 , -28 ) and ( -14 , -22 ) .

#### 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. 308 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 308.
• Every number is a factor of zero (0), since 308 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, 7, 11, 14, 22, 28, 44, 77, 154, 308 are exact divisors of 308.
• Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. Each factor divides 308 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 are all less than or equal to 308.

• What two numbers make 308?

Two numbers that make 308 are 2 and 154.

• What is prime factorization of 308?

Prime factorization of 308 is 2 x 2 x 7 x 11.

• Write some multiples of 308?

First five multiples of 308 are 616, 924, 1232, 1540.

• Which is the smallest prime factor of 308?

The smallest prime factor of 308 is 2.

• Is 308 a perfect square?

No 308 is not a perfect square.

• What is the sum of all factors of 308?

The sum of all factors of 308 is 672.

• What are factors of 308?

Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.

• How do you find factors of a negative number? ( eg. -308 )?

Factors of -308 are -1, -2, -4, -7, -11, -14, -22, -28, -44, -77, -154, -308.

• Is 308 a whole number?

Yes 308 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 308. Help him in finding the mean of 308.

Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 308 is 1 + 2 + 4 + 7 + 11 + 14 + 22 + 28 + 44 + 77 + 154 + 308 = 672.
Hence, the mean of factors of 308 is 672 ÷ 12 = 56.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 308? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
Negative factors are -1, -2, -4, -7, -11, -14, -22, -28, -44, -77, -154, -308.

Joey wants to write all the prime factors of 308 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 308 are 2, 2, 7, 11.
So in exponential form it can be written as 22 x 7 x 11.

Kevin has been asked to write 11 factor(s) of 308. Can you predict the answer?

11 factor(s) of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154.

Sammy is puzzled while calculating the prime factors of 308. Can you help him find them?

Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
Prime factors of 308 are 2, 2, 7, 11

What is prime factorization of 308?

Prime factorization of 308 is 2 x 2 x 7 x 11 = 22 x 7 x 11.

Can you help Rubel to find out the product of the even factors of 308?

Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
Even factors of 308 are 2, 4, 14, 22, 28, 44, 154, 308.
Hence, product of even factors of 308 is; 2 x 4 x 14 x 22 x 28 x 44 x 154 x 308 = 143986855936.