101 LearnersLast updated on August 5th, 2025
GCF of 16 and 56
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 16 and 56.
What is the GCF of 16 and 56?
The greatest common factor of 16 and 56 is 8. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 16 and 56?
To find the GCF of 16 and 56, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method or Euclidean Algorithm
GCF of 16 and 56 by Using Listing of Factors
Steps to find the GCF of 16 and 56 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them. Common factors of 16 and 56: 1, 2, 4, 8.
Step 3: Choose the largest factor. The largest factor that both numbers have is 8.
The GCF of 16 and 56 is 8.
GCF of 16 and 56 Using Prime Factorization
To find the GCF of 16 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 16: 16 = 2×2×2×2 = 24
Prime Factors of 56: 56 = 2×2×2×7 = 23×7
Step 2: Now, identify the common prime factors. The common prime factors are: 2×2×2 = 23
Step 3: Multiply the common prime factors. 23 = 8.
The Greatest Common Factor of 16 and 56 is 8.
GCF of 16 and 56 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 56 by 16. 56 ÷ 16 = 3 (quotient).
The remainder is calculated as 56 − (16×3) = 8.
The remainder is 8, not zero, so continue the process.
Step 2: Now divide the previous divisor (16) by the previous remainder (8).
Divide 16 by 8. 16 ÷ 8 = 2 (quotient), remainder = 16 − (8×2) = 0.
The remainder is zero, so the divisor becomes the GCF. The GCF of 16 and 56 is 8.
Common Mistakes and How to Avoid Them in GCF of 16 and 56
Finding the GCF of 16 and 56 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 16, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 16 and 56 Examples
Problem 1
A gardener has 16 rose bushes and 56 tulip bulbs. She wants to plant them in equal rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 16 and 56.
GCF of 16 and 56: 23 = 8.
There are 8 equal rows. 16 ÷ 8 = 2
56 ÷ 8 = 7
There will be 8 rows, and each row gets 2 rose bushes and 7 tulip bulbs.
Explanation
As the GCF of 16 and 56 is 8, the gardener can make 8 rows.
Now divide 16 and 56 by 8.
Each row gets 2 rose bushes and 7 tulip bulbs.
Problem 2
A teacher has two sets of markers, one with 16 red markers and the other with 56 blue markers. She wants to distribute them in packs with the same number of markers in each pack, using the largest possible number of markers per pack. How many markers will be in each pack?
GCF of 16 and 56: 23 = 8.
So each pack will have 8 markers.
Explanation
There are 16 red markers and 56 blue markers. To find the total number of markers in each pack, we should find the GCF of 16 and 56. There will be 8 markers in each pack.
Problem 3
A tailor has 16 meters of red fabric and 56 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 16 and 56.
The GCF of 16 and 56: 23 = 8.
The fabric is 8 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 16 and 56, which is 8. The length of each piece of fabric will be 8 meters.
Problem 4
A carpenter has two wooden planks, one 16 cm long and the other 56 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood. GCF of 16 and 56: 23 = 8.
The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 16 cm and 56 cm, respectively, we have to find the GCF of 16 and 56, which is 8 cm. The longest length of each piece is 8 cm.
Problem 5
If the GCF of 16 and ‘b’ is 8, and the LCM is 112. Find ‘b’.
The value of ‘b’ is 56.
Explanation
GCF x LCM = product of the numbers
8 × 112 = 16 × b
896 = 16b
b = 896 ÷ 16 = 56
FAQs on the Greatest Common Factor of 16 and 56
1.What is the LCM of 16 and 56?
2.Is 16 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 56?
5.Are 16 and 56 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 16 and 56?
7.What are some fun ways kids in United Kingdom can practice GCF of 16 and 56 with numbers?
8.What role do numbers and GCF of 16 and 56 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 16 and 56 skills?
Important Glossaries for GCF of 16 and 56
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 56 is 112.
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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.
