# Factors of 15

Factors of 15 are 1, 3, 5, and 15

#### How to find factors of a number

 1.   Find factors of 15 using Division Method 2.   Find factors of 15 using Prime Factorization 3.   Find factors of 15 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 15

• Divide 15 by 1: 15 ÷ 1 : Remainder = 0
• Divide 15 by 3: 15 ÷ 3 : Remainder = 0
• Divide 15 by 5: 15 ÷ 5 : Remainder = 0
• Divide 15 by 15: 15 ÷ 15 : Remainder = 0

Hence, Factors of 15 are 1, 3, 5, and 15

#### 2. Steps to find factors of 15 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 15 using the division method, follow these steps:

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

So, the prime factorization of 15 is, 15 = 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 15 as shown below:

So, the prime factorization of 15 is, 15 = 3 x 5.

#### 3. Find factors of 15 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 15 would be the two numbers which, when multiplied, give 15 as the result.

The following table represents the calculation of factors of 15 in pairs:

Factor Pair Pair Factorization
1 and 15 1 x 15 = 15
3 and 5 3 x 5 = 15

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 15. They are called negative pair factors.

Hence, the negative pairs of 15 would be ( -1 , -15 ) , ( -3 , -5 ) .

#### 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

• Every number is a factor of zero (0), since 15 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, 3, 5, 15 are exact divisors of 15.
• Factors of 15 are 1, 3, 5, 15. Each factor divides 15 without leaving a remainder.

• How do you find factors of a negative number? ( eg. -15 )?

Factors of -15 are -1, -3, -5, -15.

• What is the sum of all factors of 15?

The sum of all factors of 15 is 24.

• What is prime factorization of 15?

Prime factorization of 15 is 3 x 5.

• What are the pair factors of 15?

Pair factors of 15 are (1,15), (3,5).

• What are six multiples of 15?

First five multiples of 15 are 30, 45, 60, 75, 90, 105.

• Is 15 a whole number?

Yes 15 is a whole number.

• Which is the smallest prime factor of 15?

Smallest prime factor of 15 is 3.

• What are five multiples of 15?

First five multiples of 15 are 30, 45, 60, 75, 90.

• Write all factors of 15?

Factors of 15 are 1, 3, 5, 15.

#### Examples of Factors

Joey wants to write all the prime factors of 15 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 15 are 3, 5.
So in exponential form it can be written as 3 x 5.

How many factors are there for 15?

Factors of 15 are 1, 3, 5, 15.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 15. Can you predict the answer?

3 factor(s) of 15 are 1, 3, 5.

Sammy is puzzled while calculating the prime factors of 15. Can you help him find them?

Factors of 15 are 1, 3, 5, 15.
Prime factors of 15 are 3, 5

What is prime factorization of 15?

Prime factorization of 15 is 3 x 5 = 3 x 5.

Ariel has been assigned the task to find the product of all the prime factors of 15. Can you help her?

Prime factors of 15 are 3, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 15?

Factors of 15 are 1, 3, 5, 15.
Even factors of 15 are 0.
Hence, product of even factors of 15 is; 0 = 0.