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121 LearnersLast updated on August 12, 2025
GCF of 52 and 32
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 52 and 32.
What is the GCF of 52 and 32?
The greatest common factor of 52 and 32 is 4. 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 52 and 32?
To find the GCF of 52 and 32, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 52 and 32 by Using Listing of factors
Steps to find the GCF of 52 and 32 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 52 = 1, 2, 4, 13, 26, 52.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them. Common factors of 52 and 32: 1, 2, 4.
Step 3: Choose the largest factor. The largest factor that both numbers have is 4.
The GCF of 52 and 32 is 4.
GCF of 52 and 32 Using Prime Factorization
To find the GCF of 52 and 32 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 52: 52 = 2 × 2 × 13 = 2² × 13
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 = 2²
Step 3: Multiply the common prime factors. 2² = 4
The Greatest Common Factor of 52 and 32 is 4.
GCF of 52 and 32 Using Division Method or Euclidean Algorithm Method
Find the GCF of 52 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 52 by 32. 52 ÷ 32 = 1 (quotient), The remainder is calculated as 52 − (32×1) = 20. The remainder is 20, not zero, so continue the process.
Step 2: Now divide the previous divisor (32) by the previous remainder (20). Divide 32 by 20. 32 ÷ 20 = 1 (quotient), remainder = 32 − (20×1) = 12.
Step 3: Continue the process with the new divisor (20) and new remainder (12). 20 ÷ 12 = 1 (quotient), remainder = 20 − (12×1) = 8.
Step 4: Continue with the new divisor (12) and new remainder (8). 12 ÷ 8 = 1 (quotient), remainder = 12 − (8×1) = 4.
Step 5: Continue with the new divisor (8) and new remainder (4). 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0.
The remainder is zero, the divisor will become the GCF. The GCF of 52 and 32 is 4.
Common Mistakes and How to Avoid Them in GCF of 52 and 32
Finding GCF of 52 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
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 52, students may mention 6 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 between 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; 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 52 and 32 Examples
Problem 1
A florist has 52 roses and 32 tulips. She wants to create bouquets with an equal number of flowers. What is the largest number of flowers that can be in each bouquet?
We should find the GCF of 52 and 32. GCF of 52 and 32 is 4. 52 ÷ 4 = 13 32 ÷ 4 = 8 There will be 4 flowers in each bouquet.
Explanation
As the GCF of 52 and 32 is 4, the florist can make bouquets with 4 flowers each. Now divide 52 and 32 by 4. Each bouquet will have 13 roses and 8 tulips.
Problem 2
A cook has 52 apples and 32 oranges. They want to arrange them in trays with the same number of fruits in each tray, using the largest possible number of fruits per tray. How many fruits will be in each tray?
GCF of 52 and 32 is 4. So each tray will have 4 fruits.
Explanation
There are 52 apples and 32 oranges. To find the total number of fruits in each tray, we should find the GCF of 52 and 32. There will be 4 fruits in each tray.
Problem 3
A tailor has 52 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?
For calculating the longest equal length, we have to calculate the GCF of 52 and 32. The GCF of 52 and 32 is 4. The fabric pieces will be 4 meters long.
Explanation
For calculating the longest length of the fabric pieces, first we need to calculate the GCF of 52 and 32, which is 4. The length of each piece of fabric will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 52 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?
The carpenter needs the longest piece of wood. GCF of 52 and 32 is 4. The longest length of each piece is 4 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 52 cm and 32 cm, respectively, we have to find the GCF of 52 and 32, which is 4 cm. The longest length of each piece is 4 cm.
Problem 5
If the GCF of 52 and ‘a’ is 4, and the LCM is 416. Find ‘a’.
The value of ‘a’ is 32.
Explanation
GCF x LCM = product of the numbers 4 × 416 = 52 × a 1664 = 52a a = 1664 ÷ 52 = 32
FAQs on the Greatest Common Factor of 52 and 32
1.What is the LCM of 52 and 32?
2.Is 52 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 32?
5.Are 52 and 32 prime numbers?
Important Glossaries for GCF of 52 and 32
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- 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 15 are 3 and 5.
- 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.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 52 and 32 is 4, as it is their largest common factor that divides the numbers completely.
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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.
