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127 LearnersLast updated on December 11, 2025
GCF of 35 and 50
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 35 and 50.
What is the GCF of 35 and 50?
The greatest common factor of 35 and 50 is 5.
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 35 and 50?
To find the GCF of 35 and 50, a few methods are described below :-
- Listing Factors
- Prime Factorization
โโโโโโโ - Long Division Method / by Euclidean Algorithm
GCF of 35 and 50 by Using Listing of Factors
Steps to find the GCF of 35 and 50 using the listing of factors:
Step 1: Firstly, list the factors of each number. Factors of 35 = 1, 5, 7, 35. Factors of 50 = 1, 2, 5, 10, 25, 50.
Step 2: Now, identify the common factors of them. Common factors of 35 and 50: 1, 5.
Step 3: Choose the largest factor. The largest factor that both numbers have is 5.
The GCF of 35 and 50 is 5.
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GCF of 35 and 50 Using Prime Factorization
To find the GCF of 35 and 50 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number. Prime Factors of 35: 35 = 5 x 7. Prime Factors of 50: 50 = 2 x 5 x 5 = 2 x 5².
Step 2: Now, identify the common prime factors. The common prime factor is: 5.
Step 3: Multiply the common prime factors. 5 = 5. The Greatest Common Factor of 35 and 50 is 5.
GCF of 35 and 50 Using Division Method or Euclidean Algorithm Method
Find the GCF of 35 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 35. 50 ÷ 35 = 1 (quotient), The remainder is calculated as 50 − (35×1) = 15. The remainder is 15, not zero, so continue the process.
Step 2: Now divide the previous divisor (35) by the previous remainder (15). Divide 35 by 15. 35 ÷ 15 = 2 (quotient), remainder = 35 − (15×2) = 5. The remainder is 5, not zero, so continue the process.
Step 3: Divide the previous divisor (15) by the previous remainder (5). 15 ÷ 5 = 3 (quotient), remainder = 15 - (5×3) = 0. The remainder is zero, the divisor will become the GCF.
The GCF of 35 and 50 is 5.
Common Mistakes and How to Avoid Them in GCF of 35 and 50
Finding the GCF of 35 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 35, 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 indicates an incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 35 and 50 Examples
Problem 1
A gardener has 35 red roses and 50 white roses. She wants to arrange them into the largest possible equal groups. How many roses will be in each group?
We should find the GCF of 35 and 50.
GCF of 35 and 50 is 5.
There are 5 equal groups. 35 ÷ 5 = 7 and 50 ÷ 5 = 10.
There will be 5 groups, and each group gets 7 red roses and 10 white roses.
Explanation
As the GCF of 35 and 50 is 5, the gardener can make 5 groups.
Now divide 35 and 50 by 5.
Each group gets 7 red roses and 10 white roses.
Problem 2
A baker has 35 chocolate cupcakes and 50 vanilla cupcakes. He wants to pack them into boxes with the same number of cupcakes in each box, using the largest possible number of cupcakes per box. How many cupcakes will be in each box?
GCF of 35 and 50 is 5.
So each box will have 5 cupcakes.
Explanation
There are 35 chocolate and 50 vanilla cupcakes.
To find the total number of cupcakes in each box, we should find the GCF of 35 and 50.
There will be 5 cupcakes in each box.
Problem 3
A tailor has 35 meters of silk fabric and 50 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 35 and 50.
The GCF of 35 and 50 is 5.
The fabric is 5 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 35 and 50, which is 5.
The length of each piece of fabric will be 5 meters.
Problem 4
A carpenter has two wooden planks, one 35 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 35 and 50 is 5.
The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 35 cm and 50 cm, respectively, we have to find the GCF of 35 and 50, which is 5 cm.
The longest length of each piece is 5 cm.
Problem 5
If the GCF of 35 and โbโ is 5, and the LCM is 350. Find โbโ.
The value of ‘b’ is 50.
Explanation
GCF x LCM = product of the numbers
5 × 350 = 35 × b
1750 = 35b
b = 1750 ÷ 35 = 50
FAQs on the Greatest Common Factor of 35 and 50
1.What is the LCM of 35 and 50?
2.Is 35 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 50?
5.Are 35 and 50 prime numbers?
Important Glossaries for GCF of 35 and 50
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 14 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4, and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 7 is 35.
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.
