# Factors of 30

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

#### How to find factors of a number

 1.   Find factors of 30 using Division Method 2.   Find factors of 30 using Prime Factorization 3.   Find factors of 30 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 30

• Divide 30 by 1: 30 ÷ 1 : Remainder = 0
• Divide 30 by 2: 30 ÷ 2 : Remainder = 0
• Divide 30 by 3: 30 ÷ 3 : Remainder = 0
• Divide 30 by 5: 30 ÷ 5 : Remainder = 0
• Divide 30 by 6: 30 ÷ 6 : Remainder = 0
• Divide 30 by 10: 30 ÷ 10 : Remainder = 0
• Divide 30 by 15: 30 ÷ 15 : Remainder = 0
• Divide 30 by 30: 30 ÷ 30 : Remainder = 0

Hence, Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

#### 2. Steps to find factors of 30 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 30 using the division method, follow these steps:

• Step 1. Start dividing 30 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 30, which is 2. Divide 30 by 2 to obtain the quotient (15).
30 ÷ 2 = 15
• Step 3. Repeat step 1 with the obtained quotient (15).
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 30 is, 30 = 2 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 30 as shown below:

So, the prime factorization of 30 is, 30 = 2 x 3 x 5.

#### 3. Find factors of 30 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 30 would be the two numbers which, when multiplied, give 30 as the result.

The following table represents the calculation of factors of 30 in pairs:

Factor Pair Pair Factorization
1 and 30 1 x 30 = 30
2 and 15 2 x 15 = 30
3 and 10 3 x 10 = 30
5 and 6 5 x 6 = 30

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 30. They are called negative pair factors.

Hence, the negative pairs of 30 would be ( -1 , -30 ) , ( -2 , -15 ) , ( -3 , -10 ) and ( -5 , -6 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 30 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, 5, 6, 10, 15, 30 are exact divisors of 30.
• 1 is a factor of every number. Eg. 1 is a factor of 30.
• Every number is a factor of zero (0), since 30 x 0 = 0.

• What are the prime factors of 30?

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
Prime factors of 30 are 2, 3, 5.

• What two numbers make 30?

Two numbers that make 30 are 2 and 15.

• What is the greatest prime factors of 30?

The greatest prime factor of 30 is 5.

• What are factors of 30?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.

• How do you find factors of a negative number? ( eg. -30 )?

Factors of -30 are -1, -2, -3, -5, -6, -10, -15, -30.

• What are five multiples of 30?

First five multiples of 30 are 60, 90, 120, 150, 180.

• Write some multiples of 30?

First five multiples of 30 are 60, 90, 120, 150.

• Is 30 a perfect square?

No 30 is not a perfect square.

• What two numbers make 30?

Two numbers that make 30 are 2 and 15.

#### Examples of Factors

What is prime factorization of 30?

Prime factorization of 30 is 2 x 3 x 5 = 2 x 3 x 5.

Sammy is puzzled while calculating the prime factors of 30. Can you help him find them?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
Prime factors of 30 are 2, 3, 5

Kevin has been asked to write 7 factor(s) of 30. Can you predict the answer?

7 factor(s) of 30 are 1, 2, 3, 5, 6, 10, 15.

Joey wants to write all the prime factors of 30 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 30 are 2, 3, 5.
So in exponential form it can be written as 2 x 3 x 5.

How many factors are there for 30?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 30? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 10, 15, 30.
Negative factors are -1, -2, -3, -5, -6, -10, -15, -30.

Can you help Rubel to find out the product of the even factors of 30?

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
Even factors of 30 are 2, 6, 10, 30.
Hence, product of even factors of 30 is; 2 x 6 x 10 x 30 = 3600.