GCF of 10 and 50
2026-02-28 19:08 Diff
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Last updated on September 18, 2025

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 schedule events. In this topic, we will learn about the GCF of 10 and 50.

What is the GCF of 10 and 50?

The greatest common factor of 10 and 50 is 10. 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.

How to find the GCF of 10 and 50?

To find the GCF of 10 and 50, a few methods are described below 

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 10 and 50 by Using Listing of Factors

Steps to find the GCF of 10 and 50 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 10 = 1, 2, 5, 10.

Factors of 50 = 1, 2, 5, 10, 25, 50.

Step 2: Now, identify the common factors of them Common factors of 10 and 50: 1, 2, 5, 10.

Step 3: Choose the largest factor The largest factor that both numbers have is 10. The GCF of 10 and 50 is 10.

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GCF of 10 and 50 Using Prime Factorization

To find the GCF of 10 and 50 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 10: 10 = 2 x 5

Prime Factors of 50: 50 = 2 x 5 x 5

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 5

Step 3: Multiply the common prime factors 2 x 5 = 10. The Greatest Common Factor of 10 and 50 is 10.

GCF of 10 and 50 Using Division Method or Euclidean Algorithm Method

Find the GCF of 10 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 10 50 ÷ 10 = 5 (quotient),

The remainder is calculated as 50 − (10 x 5) = 0

The remainder is zero, so the divisor becomes the GCF.

The GCF of 10 and 50 is 10.

Common Mistakes and How to Avoid Them in GCF of 10 and 50

Finding the GCF of 10 and 50 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A teacher has 10 notebooks and 50 pens. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 10 and 50 GCF of 10 and 50 = 10.

There are 10 equal groups 10 ÷ 10 = 1 50 ÷ 10 = 5

There will be 10 groups, and each group gets 1 notebook and 5 pens.

Explanation

As the GCF of 10 and 50 is 10, the teacher can make 10 groups.

Now divide 10 and 50 by 10.

Each group gets 1 notebook and 5 pens.

Well explained 👍

Problem 2

A school has 10 red chairs and 50 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 10 and 50 = 10. So each row will have 10 chairs.

Explanation

There are 10 red and 50 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 10 and 50.

There will be 10 chairs in each row.

Well explained 👍

Problem 3

A tailor has 10 meters of red ribbon and 50 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 10 and 50

The GCF of 10 and 50 = 10.

The ribbon is 10 meters long.

Explanation

For calculating the longest length of the ribbon first, we need to calculate the GCF of 10 and 50, which is 10. The length of each piece of the ribbon will be 10 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 10 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 10 and 50 = 10

. The longest length of each piece is 10 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 10 cm and 50 cm, respectively, we have to find the GCF of 10 and 50, which is 10 cm.

The longest length of each piece is 10 cm.

Well explained 👍

Problem 5

If the GCF of 10 and ‘a’ is 10, and the LCM is 50. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 50.

Explanation

GCF x LCM = product of the numbers

10 x 50 = 10 x a

500 = 10a

a = 500 ÷ 10 = 50

Well explained 👍

FAQs on the Greatest Common Factor of 10 and 50

1.What is the LCM of 10 and 50?

The LCM of 10 and 50 is 50.

2.Is 10 divisible by 2?

Yes, 10 is divisible by 2 because it is an even number.

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.

4.What is the prime factorization of 50?

The prime factorization of 50 is 2 x 5 x 5.

5.Are 10 and 50 prime numbers?

No, 10 and 50 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 10 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 5 are 5, 10, 15, 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 10 are 2 and 5.
  • 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 10 and 50 is 50.

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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.