GCF of 24 and 33
2026-02-28 11:24 Diff
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Last updated on August 12, 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 to schedule events. In this topic, we will learn about the GCF of 24 and 33.

What is the GCF of 24 and 33?

The greatest common factor of 24 and 33 is 3. 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 24 and 33?

To find the GCF of 24 and 33, a few methods are described below - -

  1. Listing Factors 
  2. Prime Factorization 
  3. Long Division Method / by Euclidean Algorithm

GCF of 24 and 33 by Using Listing of Factors

Steps to find the GCF of 24 and 33 using the listing of factors:

Step 1: Firstly, list the factors of each number Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. Factors of 33 = 1, 3, 11, 33.

Step 2: Now, identify the common factors of them Common factors of 24 and 33: 1, 3.

Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 24 and 33 is 3.

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GCF of 24 and 33 Using Prime Factorization

To find the GCF of 24 and 33 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3 Prime Factors of 33: 33 = 3 × 11

Step 2: Now, identify the common prime factors The common prime factor is 3. Step 3: Multiply the common prime factor The Greatest Common Factor of 24 and 33 is 3.

GCF of 24 and 33 Using Division Method or Euclidean Algorithm Method

Find the GCF of 24 and 33 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 33 by 24 33 ÷ 24 = 1 (quotient), The remainder is calculated as 33 − (24×1) = 9 The remainder is 9, not zero, so continue the process

Step 2: Now divide the previous divisor (24) by the previous remainder (9) Divide 24 by 9 24 ÷ 9 = 2 (quotient), remainder = 24 − (9×2) = 6

Step 3: Now divide the previous divisor (9) by the previous remainder (6) Divide 9 by 6 9 ÷ 6 = 1 (quotient), remainder = 9 − (6×1) = 3

Step 4: Now divide the previous divisor (6) by the previous remainder (3) Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0

The remainder is zero, the divisor will become the GCF. The GCF of 24 and 33 is 3.

Common Mistakes and How to Avoid Them in GCF of 24 and 33

Finding the GCF of 24 and 33 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 gardener has 24 roses and 33 tulips. She wants to plant them in rows with the same number of flowers in each row. What is the maximum number of flowers she can have in each row?

Okay, lets begin

We should find the GCF of 24 and 33 GCF of 24 and 33 = 3. So each row will have 3 flowers.

Explanation

As the GCF of 24 and 33 is 3, the gardener can plant the flowers in rows with 3 flowers in each row.

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Problem 2

A chef has 24 apples and 33 oranges. He wants to create fruit baskets with the same number of fruits. What is the maximum number of fruits in each basket?

Okay, lets begin

GCF of 24 and 33 = 3. So each basket will have 3 fruits.

Explanation

There are 24 apples and 33 oranges. To find the total number of fruits in each basket, we should find the GCF of 24 and 33. There will be 3 fruits in each basket.

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Problem 3

A painter has 24 red paint tubes and 33 blue paint tubes. He wants to organize them into sets with the same number of tubes in each set. What is the largest number of tubes in each set?

Okay, lets begin

For calculating the largest equal set, we have to calculate the GCF of 24 and 33 The GCF of 24 and 33 = 3. Each set will have 3 tubes.

Explanation

For calculating the largest set of paint tubes, first, we need to calculate the GCF of 24 and 33, which is 3. The largest number of tubes in each set will be 3.

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Problem 4

A hiker has two ropes, one 24 meters long and the other 33 meters long. She wants to cut them into the longest possible equal pieces, without any rope left over. What should be the length of each piece?

Okay, lets begin

The hiker needs the longest piece of rope GCF of 24 and 33 = 3. The longest length of each piece is 3 meters.

Explanation

To find the longest length of each piece of the two ropes, 24 meters and 33 meters, respectively, we have to find the GCF of 24 and 33, which is 3 meters. The longest length of each piece is 3 meters.

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Problem 5

If the GCF of 24 and ‘b’ is 3, and the LCM is 264, find ‘b’.

Okay, lets begin

The value of ‘b’ is 33.

Explanation

GCF × LCM = product of the numbers 3 × 264 = 24 × b 792 = 24b b = 792 ÷ 24 = 33

Well explained 👍

FAQs on the Greatest Common Factor of 24 and 33

1.What is the LCM of 24 and 33?

The LCM of 24 and 33 is 264.

2.Is 33 divisible by 3?

Yes, 33 is divisible by 3 because the sum of its digits (3+3=6) is divisible by 3.

3.What will be the GCF of any two co-prime numbers?

The common factor of co-prime numbers is 1. Since 1 is the only common factor of any two co-prime numbers, it is said to be the GCF of any two co-prime numbers.

4.What is the prime factorization of 24?

The prime factorization of 24 is 2³ × 3.

5.Are 24 and 33 co-prime numbers?

No, 24 and 33 are not co-prime numbers because they have a common factor other than 1, which is 3.

Important Glossaries for GCF of 24 and 33

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
  • Multiples: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 20 are 2 and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 33 is 264.

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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.