GCF of 36 and 63
2026-02-28 13:02 Diff
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Last updated on August 5, 2025

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 36 and 63.

What is the GCF of 36 and 63?

The greatest common factor of 36 and 63 is 9. 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 36 and 63?

To find the GCF of 36 and 63, a few methods are described below:

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

GCF of 36 and 63 by Using Listing of Factors

Steps to find the GCF of 36 and 63 using the listing of factors:

Step 1: Firstly, list the factors of each number:

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 63 = 1, 3, 7, 9, 21, 63.

Step 2: Now, identify the common factors of them. Common factors of 36 and 63: 1, 3, 9.

Step 3: Choose the largest factor:

The largest factor that both numbers have is 9.

The GCF of 36 and 63 is 9.

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GCF of 36 and 63 Using Prime Factorization

To find the GCF of 36 and 63 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number:

Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²

Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7

Step 2: Now, identify the common prime factors.

The common prime factors are: 3 x 3 = 3²

Step 3: Multiply the common prime factors 3² = 9.

The Greatest Common Factor of 36 and 63 is 9.

GCF of 36 and 63 Using Division Method or Euclidean Algorithm Method

Find the GCF of 36 and 63 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number

Here, divide 63 by 36 63 ÷ 36 = 1 (quotient), The remainder is calculated as 63 − (36×1) = 27

The remainder is 27, not zero, so continue the process

Step 2: Now divide the previous divisor (36) by the previous remainder (27)

Divide 36 by 27 36 ÷ 27 = 1 (quotient), remainder = 36 − (27×1) = 9

Step 3: Now divide the previous divisor (27) by the previous remainder (9)

Divide 27 by 9 27 ÷ 9 = 3 (quotient), remainder = 27 − (9×3) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 36 and 63 is 9.

Common Mistakes and How to Avoid Them in GCF of 36 and 63

Finding the GCF of 36 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A teacher has 36 apples and 63 oranges. She wants to pack them into equal boxes with the largest number of fruits in each box. How many fruits will be in each box?

Okay, lets begin

We should find the GCF of 36 and 63.

GCF of 36 and 63

3² = 9.

There are 9 equal boxes

36 ÷ 9 = 4

63 ÷ 9 = 7

There will be 9 boxes, and each box gets 4 apples and 7 oranges.

Explanation

As the GCF of 36 and 63 is 9, the teacher can make 9 boxes.

Now divide 36 and 63 by 9.

Each box gets 4 apples and 7 oranges.

Well explained 👍

Problem 2

A school has 36 red chairs and 63 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 36 and 63

3² = 9.

So each row will have 9 chairs.

Explanation

There are 36 red and 63 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 36 and 63.

There will be 9 chairs in each row.

Well explained 👍

Problem 3

A tailor has 36 meters of silk ribbon and 63 meters of cotton 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 36 and 63

The GCF of 36 and 63

3² = 9.

The ribbon is 9 meters long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 36 and 63, which is 9. The length of each piece of the ribbon will be 9 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 36 cm long and the other 63 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 36 and 63 3² = 9.

The longest length of each piece is 9 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 36 cm and 63 cm, respectively. We have to find the GCF of 36 and 63, which is 9 cm. The longest length of each piece is 9 cm.

Well explained 👍

Problem 5

If the GCF of 36 and ‘b’ is 9, and the LCM is 252. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 63.

Explanation

GCF x LCM = product of the numbers

9 × 252 = 36 × b

2268 = 36b

b = 2268 ÷ 36 = 63

Well explained 👍

FAQs on the Greatest Common Factor of 36 and 63

1.What is the LCM of 36 and 63?

The LCM of 36 and 63 is 252.

2.Is 36 divisible by 3?

Yes, 36 is divisible by 3 because the sum of its digits (3+6) is 9, which is divisible by 3.

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 63?

The prime factorization of 63 is 3² x 7.

5.Are 36 and 63 prime numbers?

No, 36 and 63 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 36 and 63

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
  • 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.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 9 is 18.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 63 is 9, 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.