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102 LearnersLast updated on September 24, 2025
GCF of 72 and 34
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 72 and 34.
What is the GCF of 72 and 34?
The greatest common factor of 72 and 34 is 2. The largest divisor of two or more numbers is called the GCF of the numbers.
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 72 and 34?
To find the GCF of 72 and 34, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 72 and 34 by Using Listing of factors
Steps to find the GCF of 72 and 34 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 34 = 1, 2, 17, 34.
Step 2: Now, identify the common factors of them Common factors of 72 and 34: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2. The GCF of 72 and 34 is 2.
GCF of 72 and 34 Using Prime Factorization
To find the GCF of 72 and 34 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2 Prime Factors of 34: 34 = 2 x 17
Step 2: Now, identify the common prime factors The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2. The Greatest Common Factor of 72 and 34 is 2.
GCF of 72 and 34 Using Division Method or Euclidean Algorithm Method
Find the GCF of 72 and 34 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 34 72 ÷ 34 = 2 (quotient), The remainder is calculated as 72 − (34×2) = 4 The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (34) by the previous remainder (4) Divide 34 by 4 34 ÷ 4 = 8 (quotient), remainder = 34 − (4×8) = 2
Step 3: Now divide the previous divisor (4) by the previous remainder (2) Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 34 is 2.
Common Mistakes and How to Avoid Them in GCF of 72 and 34
Finding the GCF of 72 and 34 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 72, 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 72 and 34 Examples
Problem 1
A gardener has 72 tulips and 34 roses. She wants to plant them in equal groups with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 72 and 34 GCF of 72 and 34 2 = 2. There are 2 equal groups 72 ÷ 2 = 36 34 ÷ 2 = 17 There will be 2 groups, and each group gets 36 tulips and 17 roses.
Explanation
As the GCF of 72 and 34 is 2, the gardener can make 2 groups.
Now divide 72 and 34 by 2.
Each group gets 36 tulips and 17 roses.
Problem 2
A baker has 72 chocolate cupcakes and 34 vanilla cupcakes. He wants to arrange them in trays with the same number of cupcakes in each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be in each tray?
GCF of 72 and 34 2 = 2. So, each tray will have 2 cupcakes.
Explanation
There are 72 chocolate and 34 vanilla cupcakes.
To find the total number of cupcakes in each tray, we should find the GCF of 72 and 34.
There will be 2 cupcakes in each tray.
Problem 3
A tailor has 72 meters of silk fabric and 34 meters of cotton 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 72 and 34 The GCF of 72 and 34 2 = 2. The fabric is 2 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 72 and 34, which is 2.
The length of each piece of fabric will be 2 meters.
Problem 4
A carpenter has two wooden boards, one 72 cm long and the other 34 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 72 and 34 2 = 2. The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden boards, 72 cm and 34 cm, respectively.
We need to find the GCF of 72 and 34, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 72 and ‘b’ is 2, and the LCM is 612. Find ‘b’.
The value of ‘b’ is 34.
Explanation
GCF x LCM = product of the numbers
2 × 612 = 72 × b
1224 = 72b
b = 1224 ÷ 72
= 34
FAQs on the Greatest Common Factor of 72 and 34
1.What is the LCM of 72 and 34?
2.Is 72 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 34?
5.Are 72 and 34 prime numbers?
Important Glossaries for GCF of 72 and 34
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Factorization: The process of breaking down a number into its basic building blocks, which are prime numbers. For example, the prime factorization of 18 is 2 x 3^2.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 72 and 34 is 2, as it is their largest common factor that divides the numbers completely.
- 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 72 and 34 is 1224.
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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.
