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885 LearnersLast updated on December 17, 2025
Factors of 16
The factors of 16 are whole numbers that divide 16 completely with zero remainder. In daily life, we use the application of factors in packaging or arranging objects equally in a group.
What are the factors of 16
1, 2, 4, 8, and 16 are the factors of 16
Negative factors of 16: For each positive factor, there is a corresponding negative factor.
Negative factors: -1, -2, -4, -8, -16
Prime factors of 16: Prime factors are the numbers that can be divided by the number itself or 1, in case of 16, the only prime factor is 2.
Prime factorization of 16:Prime factorization is used to express the product of primes in exponential form.
16 is prime factorized as 24
The factors of 16 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 16 | 1, 2, 4, 8, 16 |
| Negative Factors of 16 | −1, −2, −4, −8, −16 |
| Prime Factors of 16 | 2 |
| Prime Factorization of 16 | 2 × 2 × 2 × 2 = 2โด |
| The sum of the Factors of 16 | 31 |
How to find the factors of 16
Students use various methods to find out the factors of a number. Here, we explain a few methods as follows -
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
Finding Factors Using Multiplication Method
In multiplication method, we find pairs of number where the product will be 16. In this process, possible steps will be -
Step 1: Find all those numbers whose product will be 16.
Step 2: These numbers will be called the factors of 16.
Step 3: Students have to write these pairs of number for this method.
List of numbers whose product is 16
1 × 16 = 16
2 × 8 = 16
4 × 4 = 16
So the pair of numbers whose product is 16 are (1,16), (2,8) and (4,4).
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Finding Factors Using Division Method
For the division method, the process of division will go on until the remainder becomes zero.
Step-by-step process:
Step 1: For division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 16÷1 = 16
Step 2: Then check with next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 16÷2 = 8 and so on.
Prime Factors and Prime Factorization
Prime factorization is the process where the number will be a product of prime factors or prime numbers.
Prime Factors of 16
Prime Factors of 16:
16 has only 2 as its prime factor.
To find the prime factor of 16:
Divide 16 by the smallest prime number 2
16÷2 = 8
8÷2 = 4
4÷2 = 2
2 ÷2 = 1
Prime Factorization of 16
In prime factorization method, 16 can also be written as 24.
Prime Factorization helps to express the prime factors in their exponential form. Prime Factorization is expressed as 24
Factor Tree
Through factor tree, the prime factors are branched out to show the process clearly for students.
Factor Tree of 16:
Factor Pairs of 16
The factors of 16 can be written in both positive and negative pairs. The table below represents the factor pairs of 16, where the product of each pair of numbers is equal to 16.
Positive Pair Factors of 16:
| Factors | Positive Pair Factors |
| 1 × 16 = 16 | 1, 16 |
| 2 × 8 = 16 | 2, 8 |
| 4 × 4 = 16 | 4, 4 |
Since the product of two negative numbers is also positive, 16 also has negative pair factors.
Negative Pair Factors of 16:
| Factors | Negative Pair Factors |
| −1 × −16 = 16 | −1, −16 |
| −2 × −8 = 16 | −2, −8 |
| −4 × −4 = 16 | −4, −4 |
Common Mistakes and How to Avoid Them in Factors of 16.
While solving factors, students may face different kinds of difficulties. Few common mistakes are seen quite frequently in factors problems -
Mistake 1
Forgetting to write 1 and 16 as factors
Students sometimes forget to write the numbers like 1 and 16 as the factors. As per the multiplication method, 1 and 16 are also the factors, as the product becomes the number itself.
Misunderstanding 42as the only factor of 16
Since 16 is a perfect square of 4, it is possible to write 4 two times in the factor list. One should remember that 4 itself can be factorized into 22 or rather can be represented as 24.
Mistake 4
Skipping prime factors
Number 16 can have prime numbers as its factor even though it is even. From the prime factorization method, it is shown 2 is the only prime factor of 16.
Examples on Factors of 16
Problem 1
Find the sum of even factors of 16
Sum is 31
Explanation
Write down the factors. Identify the even factors and add them together
Even factors of are: 2, 4, 8 and 12
Problem 2
A Costco store in Chicago is packing protein bars into equal boxes. The store has 16 protein bars and wants to divide them into equal groups with no bars left over. How many different group sizes are possible?
5
Explanation
To find all possible equal group sizes, we list the factors of 16.
The factors of 16 are 1, 2, 4, 8, and 16.
Each factor represents a valid group size.
Since there are 5 factors, there are 5 different ways to group the bars evenly.
Problem 3
What will be the greatest common factor of 16 and 12?,A pharmacist at CVS in Boston has 16 tablets of a vitamin supplement. The tablets must be split into equal daily doses for patients. Which numbers can be used as the number of tablets per dose without any tablets left?
The greatest common factor is 4
1, 2, 4, 8, 16
Explanation
To find the greatest common factor(GCF), list the factors of 16 and 12. From the factors of 16 and 12, find the biggest number, which is common in both.
Factors of 16: 1, 2, 4, 8, 16
Factors of 12: 1, 2, 3, 4, 6
Valid dose sizes must divide 16 evenly. The factors of 16 are 1, 2, 4, 8, and 16. Each of these numbers divides 16 with no remainder, so all are acceptable dosage options.
Problem 4
An NFL team traveling from Dallas to Houston receives a fuel reimbursement of $16. The team manager wants to split the amount equally among staff members. Which group sizes are possible for splitting the $16 evenly?
1, 2, 4, 8, 16
Explanation
To split money evenly, the number of people must be a factor of 16.
The factors of 16 are 1, 2, 4, 8, and 16.
These group sizes allow the $16 to be divided with no leftover amount.
FAQs on Factors of 12
1.State true or false based on the factors of 16 (a)16 is the only perfect square (b)There are 6 factors of 16
2.The product of factors of 16?
3.How do you express the Prime Factorization of 16
4.The sum of the factors of 16
5.Write the positive pair factors of 16
6.How many factors does 16 have?
7.What is the smallest factor of 16?
8.What is the largest factor of 16?
9.Which factors of 16 add up to 13?
10.How many even factors does 16 have?
11.What are the odd factors of 16?
Important Terms Related to Factors of 16
- Dividend: It is the number that is divided in the division problem. So if 16 is divided by 2, then 16 is called dividend.
- Quotient: It is the number that gets as a result of division
- Factors: Numbers that divide the given number completely without any remainder.
- Prime Factors: Prime numbers that multiply together to form the given number.
- Prime Factorization: Process of breaking down the number into prime factors
- Greatest Common Factor: Biggest factor which is common in two or more numbers.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
