# Factors of 309

Factors of 309 are 1, 3, 103, and 309

#### How to find factors of a number

 1.   Find factors of 309 using Division Method 2.   Find factors of 309 using Prime Factorization 3.   Find factors of 309 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 309

• Divide 309 by 1: 309 ÷ 1 : Remainder = 0
• Divide 309 by 3: 309 ÷ 3 : Remainder = 0
• Divide 309 by 103: 309 ÷ 103 : Remainder = 0
• Divide 309 by 309: 309 ÷ 309 : Remainder = 0

Hence, Factors of 309 are 1, 3, 103, and 309

#### 2. Steps to find factors of 309 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 309 using the division method, follow these steps:

• Step 1. Start dividing 309 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 309, which is 3. Divide 309 by 3 to obtain the quotient (103).
309 ÷ 3 = 103
• Step 3. Repeat step 1 with the obtained quotient (103).
103 ÷ 103 = 1

So, the prime factorization of 309 is, 309 = 3 x 103.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 309 as shown below:

So, the prime factorization of 309 is, 309 = 3 x 103.

#### 3. Find factors of 309 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 309 would be the two numbers which, when multiplied, give 309 as the result.

The following table represents the calculation of factors of 309 in pairs:

Factor Pair Pair Factorization
1 and 309 1 x 309 = 309
3 and 103 3 x 103 = 309

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 309. They are called negative pair factors.

Hence, the negative pairs of 309 would be ( -1 , -309 ) , ( -3 , -103 ) .

#### 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, 3, 103, 309 are exact divisors of 309.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 309 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 309.

#### Frequently Asked Questions

• What are the prime factors of 309?

The factors of 309 are 1, 3, 103, 309.
Prime factors of 309 are 3, 103.

• What two numbers make 309?

Two numbers that make 309 are 3 and 103.

• What is the greatest prime factors of 309?

The greatest prime factor of 309 is 103.

• What are factors of 309?

Factors of 309 are 1, 3, 103, 309.

• How do you find factors of a negative number? ( eg. -309 )?

Factors of -309 are -1, -3, -103, -309.

• What are five multiples of 309?

First five multiples of 309 are 618, 927, 1236, 1545, 1854.

• Write some multiples of 309?

First five multiples of 309 are 618, 927, 1236, 1545.

• Is 309 a perfect square?

No 309 is not a perfect square.

• What two numbers make 309?

Two numbers that make 309 are 3 and 103.

#### Examples of Factors

What is prime factorization of 309?

Prime factorization of 309 is 3 x 103 = 3 x 103.

Sammy is puzzled while calculating the prime factors of 309. Can you help him find them?

Factors of 309 are 1, 3, 103, 309.
Prime factors of 309 are 3, 103

Kevin has been asked to write 3 factor(s) of 309. Can you predict the answer?

3 factor(s) of 309 are 1, 3, 103.

Joey wants to write all the prime factors of 309 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 309 are 3, 103.
So in exponential form it can be written as 3 x 103.

How many factors are there for 309?

Factors of 309 are 1, 3, 103, 309.
So there are in total 4 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 309? Help her in writing all the factors.

Positive factors are 1, 3, 103, 309.
Negative factors are -1, -3, -103, -309.

Can you help Rubel to find out the product of the even factors of 309?

Factors of 309 are 1, 3, 103, 309.
Even factors of 309 are 0.
Hence, product of even factors of 309 is; 0 = 0.

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