Summarize this article:
101 LearnersLast updated on October 25, 2025
GCF of 32 and 50
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 32 and 50.
What is the GCF of 32 and 50?
The greatest common factor of 32 and 50 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 32 and 50?
To find the GCF of 32 and 50, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 32 and 50 by Using Listing of factors
Steps to find the GCF of 32 and 50 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 32 = 1, 2, 4, 8, 16, 32. Factors of 50 = 1, 2, 5, 10, 25, 50.
Step 2: Now, identify the common factors of them Common factors of 32 and 50: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2.
The GCF of 32 and 50 is 2.
GCF of 32 and 50 Using Prime Factorization
To find the GCF of 32 and 50 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2^5 Prime Factors of 50: 50 = 2 x 5 x 5 = 2 x 5^2.
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 32 and 50 is 2.
GCF of 32 and 50 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 50 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 50 by 32 50 ÷ 32 = 1 (quotient), The remainder is calculated as 50 − (32×1) = 18. The remainder is 18, not zero, so continue the process.
Step 2: Now divide the previous divisor (32) by the previous remainder (18) Divide 32 by 18 32 ÷ 18 = 1 (quotient), remainder = 32 − (18×1) = 14. The remainder is 14, not zero, continue the process.
Step 3: Now divide the previous divisor (18) by the previous remainder (14) Divide 18 by 14 18 ÷ 14 = 1 (quotient), remainder = 18 − (14×1) = 4. The remainder is 4, not zero, continue the process.
Step 4: Now divide the previous divisor (14) by the previous remainder (4) Divide 14 by 4 14 ÷ 4 = 3 (quotient), remainder = 14 − (4×3) = 2. The remainder is 2, not zero, continue the process.
Step 5: 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 32 and 50 is 2.
Common Mistakes and How to Avoid Them in GCF of 32 and 50
Finding GCF of 32 and 50 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 32, 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 tells about the 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 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 32 and 50 Examples
Problem 1
An artist has 32 brushes and 50 tubes of paint. She wants to create sets with the largest number of items in each set. How many items will be in each set?
We should find GCF of 32 and 50 GCF of 32 and 50 is 2.
There are 2 equal sets 32 ÷ 2 = 16 50 ÷ 2 = 25.
There will be 2 sets, and each set gets 16 brushes and 25 tubes of paint.
Explanation
As the GCF of 32 and 50 is 2, the artist can make 2 sets.
Now divide 32 and 50 by 2.
Each set gets 16 brushes and 25 tubes of paint.
Problem 2
A gardener has 32 flower pots and 50 bags of soil. She wants to arrange them in groups with the same number of items in each group, using the largest possible number of items per group. How many items will be in each group?
GCF of 32 and 50 is 2.
So each group will have 2 items.
Explanation
There are 32 flower pots and 50 bags of soil.
To find the total number of items in each group, we should find the GCF of 32 and 50.
There will be 2 items in each group.
Problem 3
A chef has 32 apples and 50 oranges. She wants to pack them into boxes of equal size, using the longest possible size. What should be the number of each fruit in each box?
For calculating the longest equal size, we have to calculate the GCF of 32 and 50, The GCF of 32 and 50 is 2.
Each box will have 2 apples and 2 oranges.
Explanation
For calculating the longest size of the box first we need to calculate the GCF of 32 and 50 which is 2.
Each box will have 2 apples and 2 oranges.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 50 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 32 and 50 is 2.
The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 32 cm and 50 cm, respectively.
We have to find the GCF of 32 and 50, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 32 and ‘b’ is 2, and the LCM is 800. Find ‘b’.
The value of ‘b’ is 50.
Explanation
GCF × LCM = product of the numbers 2 × 800 = 32 × b 1600 = 32b b = 1600 ÷ 32 = 50
FAQs on the Greatest Common Factor of 32 and 50
1.What is the LCM of 32 and 50?
2.Is 32 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 50?
5.Are 32 and 50 prime numbers?
Important Glossaries for GCF of 32 and 50
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 32 are 1, 2, 4, 8, 16, 32.
- Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 50 is 2 x 5^2.
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 32 and 50 is 2.
- Euclidean Algorithm: A method for finding the greatest common factor by dividing and taking remainders.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 32 and 50 is 800.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 32 and 50
![Important Math Links Icon]()
Next to GCF of 32 and 50
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.
