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Factors of 16: Prime factorization, Methods, Tree, and Examples

A factor in mathematics is always a whole number that divides another number and gives off no remainder i.e. remainder will always be zero. Factors of 16 are the numbers that are completely divisible by the number itself. 

Factors of sixteen

Figure 1 – All possible Factors of 16

There are two super easy methods to find factors of a specific number. We can either use multiplication or division. To find factors, the rules of divisibility should always be kept in mind.

The factors of 16 will either be less than or equal to the number itself. Thus, a fact is that the factors of the number will always be less than half of that number or the exact half too.

The factors of 16 will be the numbers between 1 to 8. Finding factors of a number can also help to simplify and solve algebraic expressions. If you want to use the method of division to find factors of a specific number it can be done by dividing 16.

If the division gives no process and the answer is in whole numbers, both the divisor and quotient are considered factors.

If both the divisor and quotient are considered as factors it is called a ‘Factor pair’. However, when we write the number, i.e. 16 as a product of every prime factor, it is called prime factorization.

A fun fact is that 2 is a factor of all even numbers so, if we divide 16 by the number 2 the answer will be 8 and no remainder will be left. So in this case both 2 and 8 will be considered as the factors of 16 and will also be a factor pair. 

In this following article, you will get to read about both the possible ways in which we can find the factors of a specific number, a few fun facts about the number and you will also get to see the factor tree of the number 16. Let’s get started. 

What Are the Factors of 16?

The number 16 has 5 factors that are  1, 2, 4, 8, and 16. In addition to this, every number has negative factors as well. These numbers give zero as a remainder. 

To find negative factors of a specific number you just have to reverse the sign. Thus, the negative factors of 16 are -1, -2, -4, -8, and -16.

How to Calculate Factors of 16?

You can calculate the factors of 16 by two methods — multiplication and division. 

As 16 is a composite number, it means it is supposed to have more than 2 factors. You first have to start dividing the number with numbers between 1 to 8. Remember to only perform division of the number till 8 as a factor can not be a number more than half. 

Let’s take a few examples of the division of 16 with numbers:

\[ \frac {16}{2} = 8 \]

\[ \frac {16}{3} = 5.333.. \]

The second division doesn’t have a factor of 16 because of 2 reasons:

  1. It gives off a remainder.
  2. The answer to the division is not a whole number/ integer. 

Not to forget that if the remainder is 0 after the division has been done, the divisor and quotient both will be considered as factors and will make a factor pair.

Hence, 8 is a factor of 16 too. All the possible divisions are mentioned below:

\[ \frac{16}{1} = 16 \]

\[ \frac{16}{2} = 8 \]

\[ \frac{8}{4} = 2 \]

Thus, the factors of the number 16 are given below.

Factors: 1, 2, 4, 8, 16 

As each of these divisions gives no remainder and is completely divisible by 16.

Finding the factors of a number through multiplication is as easy as this one. Find two numbers that when divided together, answer 16 e.g. 2 multiplied by 8 gives 16 as the answer. As we all know that two can only be divided by 1 or itself as it’s a prime factor, it can’t be factorized further.

In such a case, we have to look at the other number we are multiplying together i.e. 8. It can be factorized till we get an answer as it is a composite number, which means that it has more than two factors. So in conclusion the factorization of 16 is:

2 x 2 x 2 x 2 = 16 

Factors of 16 by Prime Factorization

Expressing a number as a product of its prime factors is called prime factorization.

It is a method in which we multiply prime numbers to obtain the product of the number. So, while we do prime factorization, you have to keep breaking the quotient until the number 1 becomes your answer. 

For the number 16, 2 will be your first choice as a prime number as selecting the smallest possible prime number is required. 2 is a prime number as it can only be divided by 1 or the number itself. Thus the division will look like this:

\[ \frac{16}{2} = 8 \]

The same process will be continued till 1 becomes our answer. 

\[ \frac{8}{2} = 4 \]

\[ \frac{4}{2} = 2 \]

\[ \frac{2}{2} = 1 \]

Thus, it is confirmed that 2 is a prime factor of 16. The prime factorization of 16 can be mathematically written as:

\[ 2^{4} = 16 \]

 The prime factorization is shown in the diagram below as well.

Prime factorization of sixteen

Figure 2 – Prime Factorization of 16

Factor Tree of 16

Just like we can represent the prime factors of a number through the diagram above, a factor tree is another way to represent the factors of a specific number through its branches. Once the factors can’t be factorized anymore, the branches are made no further. 

Prime factorization can be done by making a factor tree for a number. 

According to prime factorization, 2 is the only prime factor of the number 16. So, when simplified, 2 will be the last number on both branches of the factor tree.  The factor tree of the number 16 can be seen below:

Factor tree of sixteen

Figure 3 – Factor Tree of 16

Factors of 16 in Pairs

A factor pair is made when a number is divided by 16 and the remainder is zero and the answer is in whole numbers. In such a case, the quotient and divisor both are considered factors of the specific number and are called a Factor pair

The number 16 is called the product and the two numbers we get are factors of the number. To find factor pairs step number one is to find all the factors of 16. You can find them by any one of the methods mentioned at the start of this article.

Once you have all the factors, start multiplying them with each other and the ones that answer 16 will be considered as a factor pair of the number 16. The factor pairs of 16 are (1, 16), (2, 8), and (4, 4).

The negative factor pairs can also be written as they are nothing but the same factors with negative signs. The negative factor pairs of 16 are (-1, -16), (-2, -8), and (-4, -4).

Factors of 16 Solved Examples

To further strengthen our concept of the factors of 16, let’s consider some examples given below.

Example 1

What are the common factors of 12 and 16?

Solution

To find the common factors of two numbers you first have to list all the factors of both the numbers and then start circling out the ones in common. 

The factors of 16 are:

Factors: 1, 2, 4, 8, 16

Whereas the factors of 12 are:

Factors:  1, 2, 3, 4, 6, 12

Thus, the common factors of the numbers 12 and 16 are:

Common Factors: 1, 2, 4 

Example 2

What is the sum of factors of 16?

Solution

A fact to remember when such a question comes up is that the keyword for addition is ‘sum’ and when you are required to subtract the keyword ‘difference’ will be given in the question. 

As of now we already know that the factors of 16 are 1, 2, 4, 8, and 16.

Thus, we are simply required to add up all these factors together to get the answer.

Hence, the sum of factors of 16 is:

 Sum of factors= 1 + 2 + 4 + 8 + 16

Sum =31

Example 3

Can you help Anna list the factors of 24 and check if the numbers 24 and 16 have any factors in common?

Solution

To get a solution to this question you have to list down all the factors of 24 and 16. There are eight factors of 24 and the number 16 has 5 factors. The factors of both the numbers are as follow:

Factors of 16: 1, 2, 4, 8, 16 

Factors: 1, 2, 3, 4, 6, 8, 12, 24 

Once you’re done listing down all the factors either cancel out the ones that are not common or circle the common factors of both the numbers.

24 and 16 have 4 factors in common that are 1, 2, 4, and 8.

All images/mathematical drawings are made by using GeoGebra.

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