Factors

# Factors of 16 | Prime Factorization of 16 | Factor Tree of 16

Written by Prerit Jain

Updated on: 05 Aug 2024

### Factors of 16 | Prime Factorization of 16 | Factor Tree of 16

The factors of 16 are the numbers that produce the result of 16 when two numbers are multiplied together.

There are a total of five factors for the 16. Factors of 16 are 1, 2, 4, 8, and 16.

In this article, we will discuss how to find factors of 16 using simple mathematical methods!

## What Is a Factor?

A factor is a number that divides another number, leaving no remainder. If we multiply two whole numbers, it gives us a product. The numbers we are multiplying are factors of the product because they are divisible by the product. Let’s learn how to find the factors of 16 using simple mathematical methods!

## What Are the Factors of 16?

The factors of 16 are the numbers that divide the number 16 without leaving any remainder. The factors of a number can be both positive and negative. Similarly, the factors of number 16 have both positive and negative factors.

## What Are the Factors of 16 in Pairs?

As above mentioned pair factors of 16 can be positive and negative. A pair factor of 16 is a combination of two numbers. For example, if (4, 4) is a positive pair, when we multiply the pair numbers, the result obtained will be 16. Similarly, when we multiply the pair factors of 16, it gives the original product 16.

## How to Find the Factors of 16?

The factors of 16 can be found using three simple mathematical methods, such as

1. Division method
2. Prime factorization method and
3. Factor tree method.

We will explain to you all three methods with proper definitions and methods.

### How to Find Factors of 16 Through the Division Method?

The numbers that divide the number 16 completely without leaving any remainder are known as factors of 16. This method helps to extract the factors of 16 by dividing the number 16 by a sequence of natural numbers.

• 16÷ 1 = 12
• 16÷ 2 = 8
• 16 ÷ 4 = 4
• 16÷ 8 = 2
• 16÷ 16 = 1

Hence, using the division method we came to the conclusion that the factors of 16 are 1, 2, 4, 8, and 16

### How to find Factors of 16 using the Prime Factorization Method?

Check whether 16 is a prime number or a composite number. If 16 is a prime number, it consists of only two factors. When it is a composite number, it means it contains more than two factors. Here, 16 is a composite number, so it has more than two factors.

We provided you with the steps to find factors of 16 using the prime factorization method for better understanding.

• Step 1: Divide the number 16 by the smallest prime number that is divisible by 16. Hence, the smallest prime number that is divisible by 16 is
16 ÷ 2 = 8
• Step 2: Now, divide the number 8 (quotient) by the smallest prime number, which is
8 ÷ 2 = 4
• Step 3: Again divide 4 by 2 and the process continues.
4 ÷ 2 = 2
2 ÷ 2 = 1

Finally, we get the result “1” at the end of the process. Here we successfully found the prime factors of 16as 2 × 2 × 2 x 2 using 2 as the prime number.

### What Is the Factor Tree of 16?

A factor tree is a unique method that is quite interesting! Let’s assume 16 is the top factor of a tree. Then write down the set of pair factors of the given number 16. Again split the factors into factors. Continue this process until the set of pair factors become prime numbers. Now identifying all the prime numbers will give us the prime factor of 16.

• Step 1: Let’s place the 16 as a top factor of the tree.
• Step 2: Multiply with the prime number that gives the result of 16. (2*8=16). Here prime number 2 is multiplied by 8 to get the result 16.
• Step 3: Since 2 is the prime number, we have to divide 8 into 4*2.
• Step 4: Now we have to leave 2 again and break 4 as 2*2. Here the factor tree of 16=2×2×2×2=24

## Solved Example Problems on Factor 16

Problem 1: What is the sum of all the factors of 16?
Solution:
Find the factors of 16.
Once you find all the factor numbers of 16.
Add the factor numbers to get the sum of all the factors of 16.
The sum of all the factors of 16 is 1+2+4+8+16=31.

Problem 2: Difference between positive factors and negative factors of 16?
Solution:
The difference between positive and negative factors The positive factors are represented using the plus(+) symbol and the negative factors are represented using the minus(-) symbol.
Examples
Positive factors: 1, 2, 4, 8, and 16.
Negative factors: -1, -2, -4, -8, and 16

Problem 3: Why is 16 a composite number?
Solution:
Prime numbers have only two factors, 1 and the number itself.
Example: The number 7 is a prime number because it is completely divisible by only 1 and 7.
Composite numbers are numbers that have more than two factors.
Example: The number 16 is divisible by 1, 2, 4, and 8.
Since 16 has more than two factors, it is considered a composite number.

Problem 4: Find the common factor of 16 and 15.
Solution:
To find common factors, list the factors of 15 and 16 separately and compare them. Now find the common factors of 16 and 15.
The factors of 16 are 1, 2, 4, 8, and 16.
The factors of 15 are 1, 3, 5, and 15.
Here, the common factor of 16 and 15 is “1”. Hence, “1” is the common factor of 16 and 15.

Problem 5: What are the factors of 16 and 24?
Solution:

If you divide the lowest prime number by 16 and 24 you will get the factors of 16 and 24.
Example :
To find factors of 16, divide 16 by the least prime number, such as 2.
16 ÷ 2 = 8
Again, divide 8 by 2 and the process goes on.
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Hence, the factors of 16 are 1, 2, 4, and 8.

## FAQs on Factors of 16

What are the prime factors of 16?
The prime factors of 16 as a product can be written as 2 × 2 × 2 x 2 or 2, where 2 is the prime number.

Are all factors of 16 even?
Except for 1, all the factors of 16 are even.

Is 16 a composite number?
The number 16 contains more than two factors. Hence, it is called a composite number.

What are the common factors of 16 and 24?
The common factors of 16 and 24 are 1, 2,4, and 8.

How many factors of 15 are also common to the factors of 16?
Since the factors of 16 are 1, 2, 4, 8, 16, and factors of 15 are 1, 3, 5, 15. Hence, 16 and 15 have only one common factor which is 1. Therefore, 16 and 15 are co-prime.

We hope that we have taught you a new concept about factors of 16 and provided you with the necessary information about factors of 16.

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Prerit Jain

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