GCF of 36 and 3
2026-02-28 10:10 Diff
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Last updated on September 24, 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 36 and 3.

What is the GCF of 36 and 3?

The greatest common factor of 36 and 3 is 3. 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 3?

To find the GCF of 36 and 3, a few methods are described below:

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

GCF of 36 and 3 by Using Listing of Factors

Steps to find the GCF of 36 and 3 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 3 = 1, 3.

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

Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 36 and 3 is 3.

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GCF of 36 and 3 Using Prime Factorization

To find the GCF of 36 and 3 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime Factors of 36: 36 = 2 × 2 × 3 × 3 = 2² × 3² Prime Factors of 3: 3 = 3¹

Step 2: Now, identify the common prime factors The common prime factor is: 3¹

Step 3: Multiply the common prime factors 3¹ = 3. The Greatest Common Factor of 36 and 3 is 3.

GCF of 36 and 3 Using Division Method or Euclidean Algorithm Method

Find the GCF of 36 and 3 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 36 by 3 36 ÷ 3 = 12 (quotient), The remainder is calculated as 36 − (3 × 12) = 0

Since the remainder is zero, the divisor will become the GCF. The GCF of 36 and 3 is 3.

Common Mistakes and How to Avoid Them in GCF of 36 and 3

Finding the GCF of 36 and 3 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 baker has 36 cookies and 3 trays. She wants to distribute the cookies equally among the trays, using the largest number of cookies per tray. How many cookies will be in each tray?

Okay, lets begin

We should find the GCF of 36 and 3. GCF of 36 and 3 is 3. 36 ÷ 3 = 12 There will be 12 cookies in each tray.

Explanation

As the GCF of 36 and 3 is 3, the baker can distribute the cookies equally among the trays.

Each tray will have 12 cookies.

Well explained 👍

Problem 2

A school has 36 desks and 3 classrooms. They want to arrange them with the same number of desks in each classroom, using the largest possible number of desks per classroom. How many desks will be in each classroom?

Okay, lets begin

GCF of 36 and 3 is 3. So each classroom will have 12 desks.

Explanation

There are 36 desks and 3 classrooms.

To find the total number of desks in each classroom, we should find the GCF of 36 and 3.

Each classroom will have 12 desks.

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Problem 3

A florist has 36 roses and 3 vases. She wants to arrange them in the vases with the same number of roses in each vase, using the largest possible number of roses per vase. How many roses will be in each vase?

Okay, lets begin

For an equal arrangement, we have to calculate the GCF of 36 and 3. The GCF of 36 and 3 is 3. Each vase will have 12 roses.

Explanation

For the equal arrangement of roses in the vases, first, we need to calculate the GCF of 36 and 3, which is 3.

Each vase will have 12 roses.

Well explained 👍

Problem 4

A tailor has a piece of fabric 36 meters long and wants to cut it into pieces of equal length that are each 3 meters long. How many pieces will she have?

Okay, lets begin

The tailor needs the longest piece of fabric. GCF of 36 and 3 is 3. The fabric will be cut into 12 pieces.

Explanation

To cut the fabric into the longest equal pieces, we need to find the GCF of 36 and 3, which is 3.

Therefore, the fabric will be cut into 12 pieces.

Well explained 👍

Problem 5

If the GCF of 36 and ‘b’ is 3, and the LCM is 108, find ‘b’.

Okay, lets begin

The value of ‘b’ is 9.

Explanation

GCF × LCM = product of the numbers

3 × 108 = 36 × b

324 = 36b

b = 324 ÷ 36

= 9

Well explained 👍

FAQs on the Greatest Common Factor of 36 and 3

1.What is the LCM of 36 and 3?

The LCM of 36 and 3 is 36.

2.Is 36 divisible by 3?

Yes, 36 is divisible by 3 because 36 ÷ 3 = 12.

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 3?

The prime factorization of 3 is 3¹.

5.Are 36 and 3 prime numbers?

No, 36 and 3 are not both prime numbers; only 3 is a prime number because it has exactly two distinct positive divisors: 1 and 3.

Important Glossaries for GCF of 36 and 3

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
  • Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factor of 3 is 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 36 and 3 is 36.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 3 is 3, 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.