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101 LearnersLast updated on September 9, 2025
GCF of 16 and 72
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 schedule events. In this topic, we will learn about the GCF of 16 and 72.
What is the GCF of 16 and 72?
The greatest common factor of 16 and 72 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 72?
To find the GCF of 16 and 72, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 16 and 72 by Using Listing of factors
Steps to find the GCF of 16 and 72 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 16 = 1, 2, 4, 8, 16. Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Step 2: Now, identify the common factors of them Common factors of 16 and 72: 1, 2, 4, 8.
Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 16 and 72 is 8.
GCF of 16 and 72 Using Prime Factorization
To find the GCF of 16 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 2⁴ Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 2³
Step 3: Multiply the common prime factors 2³ = 8. The Greatest Common Factor of 16 and 72 is 8.
GCF of 16 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 72 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 72 by 16 72 ÷ 16 = 4 (quotient), The remainder is calculated as 72 − (16×4) = 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, the divisor will become the GCF.
The GCF of 16 and 72 is 8.
Common Mistakes and How to Avoid Them in GCF of 16 and 72
Finding the GCF of 16 and 72 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 tells about the incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and 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 that 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 72 Examples
Problem 1
A gardener has 16 rose bushes and 72 tulip bulbs. She wants to plant them in equal groups with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 16 and 72 GCF of 16 and 72 2³ = 8. There are 8 equal groups 16 ÷ 8 = 2 72 ÷ 8 = 9 There will be 8 groups, and each group gets 2 rose bushes and 9 tulip bulbs.
Explanation
As the GCF of 16 and 72 is 8, the gardener can make 8 groups.
Now divide 16 and 72 by 8.
Each group gets 2 rose bushes and 9 tulip bulbs.
Problem 2
A chef has 16 eggs and 72 slices of bread. He wants to create sandwiches with the same number of eggs and slices in each batch, using the maximum possible number of eggs per batch. How many eggs will be in each batch?
GCF of 16 and 72 2³ = 8. So each batch will have 8 eggs.
Explanation
There are 16 eggs and 72 slices of bread.
To find the total number of eggs in each batch, we should find the GCF of 16 and 72.
There will be 8 eggs in each batch.
Problem 3
A farmer has 16 meters of fence and 72 square meters of field. She wants to split the field into sections with the longest possible equal perimeter. What should be the perimeter of each section?
For calculating the longest equal perimeter, we have to calculate the GCF of 16 and 72 The GCF of 16 and 72 2³ = 8. The perimeter of each section is 8 meters.
Explanation
For calculating the longest perimeter of the sections, we first need to calculate the GCF of 16 and 72, which is 8.
The perimeter of each section will be 8 meters.
Problem 4
A carpenter has two wooden pieces, one 16 cm long and the other 72 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 72 2³ = 8. The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two wooden pieces, 16 cm and 72 cm, respectively.
We have to find the GCF of 16 and 72, 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 144. Find ‘b’.
The value of ‘b’ is 72.
Explanation
GCF x LCM = product of the numbers
8 × 144
= 16 × b 1152
= 16b b
= 1152 ÷ 16 = 72
FAQs on the Greatest Common Factor of 16 and 72
1.What is the LCM of 16 and 72?
2.Is 16 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 16 and 72 prime numbers?
Important Glossaries for GCF of 16 and 72
- 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 4 are 4, 8, 12, 16, 20, 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 72 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 72 is 144.
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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.
