# Factors of 306

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306

#### How to find factors of a number

 1.   Find factors of 306 using Division Method 2.   Find factors of 306 using Prime Factorization 3.   Find factors of 306 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 306

• Divide 306 by 1: 306 ÷ 1 : Remainder = 0
• Divide 306 by 2: 306 ÷ 2 : Remainder = 0
• Divide 306 by 3: 306 ÷ 3 : Remainder = 0
• Divide 306 by 6: 306 ÷ 6 : Remainder = 0
• Divide 306 by 9: 306 ÷ 9 : Remainder = 0
• Divide 306 by 17: 306 ÷ 17 : Remainder = 0
• Divide 306 by 18: 306 ÷ 18 : Remainder = 0
• Divide 306 by 34: 306 ÷ 34 : Remainder = 0
• Divide 306 by 51: 306 ÷ 51 : Remainder = 0
• Divide 306 by 102: 306 ÷ 102 : Remainder = 0
• Divide 306 by 153: 306 ÷ 153 : Remainder = 0
• Divide 306 by 306: 306 ÷ 306 : Remainder = 0

Hence, Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306

#### 2. Steps to find factors of 306 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 306 using the division method, follow these steps:

• Step 1. Start dividing 306 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 306, which is 2. Divide 306 by 2 to obtain the quotient (153).
306 ÷ 2 = 153
• Step 3. Repeat step 1 with the obtained quotient (153).
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1

So, the prime factorization of 306 is, 306 = 2 x 3 x 3 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 306 as shown below:

So, the prime factorization of 306 is, 306 = 2 x 3 x 3 x 17.

#### 3. Find factors of 306 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 306 would be the two numbers which, when multiplied, give 306 as the result.

The following table represents the calculation of factors of 306 in pairs:

Factor Pair Pair Factorization
1 and 306 1 x 306 = 306
2 and 153 2 x 153 = 306
3 and 102 3 x 102 = 306
6 and 51 6 x 51 = 306
9 and 34 9 x 34 = 306
17 and 18 17 x 18 = 306

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 306. They are called negative pair factors.

Hence, the negative pairs of 306 would be ( -1 , -306 ) , ( -2 , -153 ) , ( -3 , -102 ) , ( -6 , -51 ) , ( -9 , -34 ) and ( -17 , -18 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 306 is a factor of itself.
• 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, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306 are exact divisors of 306.
• 1 is a factor of every number. Eg. 1 is a factor of 306.
• Every number is a factor of zero (0), since 306 x 0 = 0.

• Which is the smallest prime factor of 306?

Smallest prime factor of 306 is 2.

• Is 306 a perfect square?

No 306 is not a perfect square.

• What are five multiples of 306?

First five multiples of 306 are 612, 918, 1224, 1530, 1836.

• What is prime factorization of 306?

Prime factorization of 306 is 2 x 3 x 3 x 17.

• What are factors of 306?

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.

• How do you find factors of a negative number? ( eg. -306 )?

Factors of -306 are -1, -2, -3, -6, -9, -17, -18, -34, -51, -102, -153, -306.

• Is 306 a whole number?

Yes 306 is a whole number.

• Which is greatest factor of 306?

The greatest factor of 306 is 153.

• What are the prime factors of 306?

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Prime factors of 306 are 2, 3, 3, 17.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 306. Can you help her?

Prime factors of 306 are 2, 3, 3, 17.
Hence, the product of prime factors of 102.

Can you help Rubel to find out the product of the even factors of 306?

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Even factors of 306 are 2, 6, 18, 34, 102, 306.
Hence, product of even factors of 306 is; 2 x 6 x 18 x 34 x 102 x 306 = 229220928.

Joy wants to calculate mean of all the factors of 306. Help him in finding the mean of 306.

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 306 is 1 + 2 + 3 + 6 + 9 + 17 + 18 + 34 + 51 + 102 + 153 + 306 = 702.
Hence, the mean of factors of 306 is 702 ÷ 12 = 58.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 306? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Negative factors are -1, -2, -3, -6, -9, -17, -18, -34, -51, -102, -153, -306.

How many factors are there for 306?

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
So there are in total 12 factors.

Joey wants to write all the prime factors of 306 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 306 are 2, 3, 3, 17.
So in exponential form it can be written as 2 x 32 x 17.

Kevin has been asked to write 11 factor(s) of 306. Can you predict the answer?

11 factor(s) of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153.