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Last updated on September 10, 2025

GCF of 72 and 32

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The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 72 and 32.

GCF of 72 and 32 for US Students
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What is the GCF of 72 and 32?

The greatest common factor of 72 and 32 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.

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How to find the GCF of 72 and 32?

To find the GCF of 72 and 32, a few methods are described below -

 

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm
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GCF of 72 and 32 by Using Listing of Factors

Steps to find the GCF of 72 and 32 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 32 = 1, 2, 4, 8, 16, 32.

 

Step 2: Now, identify the common factors of them Common factors of 72 and 32: 1, 2, 4, 8.

 

Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 72 and 32 is 8.

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GCF of 72 and 32 Using Prime Factorization

To find the GCF of 72 and 32 using the Prime Factorization Method, follow these steps:

 

Step 1: Find the prime factors of each number Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3² Prime Factors of 32: 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

 

Step 2: Now, identify the common prime factors The common prime factor is: 2 × 2 × 2 = 2³

 

Step 3: Multiply the common prime factors 2³ = 8. The Greatest Common Factor of 72 and 32 is 8.

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GCF of 72 and 32 Using Division Method or Euclidean Algorithm Method

Find the GCF of 72 and 32 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 32 72 ÷ 32 = 2 (quotient), The remainder is calculated as 72 − (32×2) = 8 The remainder is 8, not zero, so continue the process

 

Step 2: Now divide the previous divisor (32) by the previous remainder (8) Divide 32 by 8 32 ÷ 8 = 4 (quotient), remainder = 32 − (8×4) = 0

 

The remainder is zero, the divisor will become the GCF. The GCF of 72 and 32 is 8.

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Common Mistakes and How to Avoid Them in GCF of 72 and 32

Finding GCF of 72 and 32 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Mistake 1

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Listing Incorrect Factors

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Students may sometimes list incorrect factors. For example, while listing factors of 72, students may mention 5, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.

Mistake 2

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Choosing the Wrong Common Factor

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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

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Forgetting to Include 1 as a Factor

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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

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Using Multiples Instead of Factors

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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

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Assuming GCF is Always an Even Number

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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.

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Greatest Common Factor of 72 and 32 Examples

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Problem 1

A gardener has 72 roses and 32 lilies. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?

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We should find the GCF of 72 and 32 GCF of 72 and 32 2³ = 8.

 

There are 8 flowers in each bouquet. 72 ÷ 8 = 9 32 ÷ 8 = 4

 

There will be 8 bouquets, with each bouquet containing 9 roses and 4 lilies.

Explanation

As the GCF of 72 and 32 is 8, the gardener can make 8 bouquets. Now divide 72 and 32 by 8. Each bouquet gets 9 roses and 4 lilies.

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Problem 2

A chef has 72 apples and 32 oranges. They want to create fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?

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GCF of 72 and 32 2³ = 8. So each basket will have 8 fruits.

Explanation

There are 72 apples and 32 oranges.

 

To find the total number of fruits in each basket, we should find the GCF of 72 and 32.

 

There will be 8 fruits in each basket.

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Problem 3

A tailor has 72 meters of red fabric and 32 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?

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For calculating the longest equal length, we have to calculate the GCF of 72 and 32 The GCF of 72 and 32

 

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 72 and 32, which is 8. The length of each piece of the fabric will be 8 meters.

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Problem 4

A carpenter has two wooden planks, one 72 cm long and the other 32 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?

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The carpenter needs the longest piece of wood GCF of 72 and 32 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, 72 cm and 32 cm, respectively. We have to find the GCF of 72 and 32, which is 8 cm. The longest length of each piece is 8 cm.

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Problem 5

If the GCF of 72 and ‘a’ is 8, and the LCM is 288. Find ‘a’.

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The value of ‘a’ is 32.

Explanation

GCF × LCM = product of the numbers

 

8 × 288 = 72 × a

 

2304 = 72a

 

a = 2304 ÷ 72 = 32

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FAQs on the Greatest Common Factor of 72 and 32

1.What is the LCM of 72 and 32?

The LCM of 72 and 32 is 288.

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2.Is 72 divisible by 2?

Yes, 72 is divisible by 2 because it is an even number.

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3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

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4.What is the prime factorization of 32?

The prime factorization of 32 is 2⁵.

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5.Are 72 and 32 prime numbers?

No, 72 and 32 are not prime numbers because both of them have more than two factors.

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Important Glossaries for GCF of 72 and 32

  • 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 8 are 8, 16, 24, 32, 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 18 are 2 and 3.

 

  • 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 72 and 32 is 288.
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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.

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Fun Fact

: She loves to read number jokes and games.

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