GCF of 33 and 15
2026-02-28 17:34 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 33 and 15.

What is the GCF of 33 and 15?

The greatest common factor of 33 and 15 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 33 and 15?

To find the GCF of 33 and 15, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm

GCF of 33 and 15 by Using Listing of Factors

Steps to find the GCF of 33 and 15 using the listing of factors Step 1: Firstly, list the factors of each number Factors of 33 = 1, 3, 11, 33. Factors of 15 = 1, 3, 5, 15. Step 2: Now, identify the common factors of them Common factors of 33 and 15: 1, 3. Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 33 and 15 is 3.

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GCF of 33 and 15 Using Prime Factorization

To find the GCF of 33 and 15 using the Prime Factorization Method, follow these steps: Step 1: Find the prime factors of each number Prime Factors of 33: 33 = 3 x 11 Prime Factors of 15: 15 = 3 x 5 Step 2: Now, identify the common prime factors The common prime factor is: 3 Step 3: Multiply the common prime factors 3 = 3 The Greatest Common Factor of 33 and 15 is 3.

GCF of 33 and 15 Using Division Method or Euclidean Algorithm Method

Find the GCF of 33 and 15 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 15 33 ÷ 15 = 2 (quotient), The remainder is calculated as 33 − (15×2) = 3 The remainder is 3, not zero, so continue the process Step 2: Now divide the previous divisor (15) by the previous remainder (3) Divide 15 by 3 15 ÷ 3 = 5 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF. The GCF of 33 and 15 is 3.

Common Mistakes and How to Avoid Them in GCF of 33 and 15

Finding the GCF of 33 and 15 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 33 notebooks and 15 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 33 and 15. GCF of 33 and 15 is 3. There are 3 equal groups. 33 ÷ 3 = 11 15 ÷ 3 = 5 There will be 3 groups, and each group gets 11 notebooks and 5 pens.

Explanation

As the GCF of 33 and 15 is 3, the teacher can make 3 groups. Now divide 33 and 15 by 3. Each group gets 11 notebooks and 5 pens.

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Problem 2

A school has 33 red flags and 15 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?

Okay, lets begin

GCF of 33 and 15 is 3. So each row will have 3 flags.

Explanation

There are 33 red and 15 blue flags. To find the total number of flags in each row, we should find the GCF of 33 and 15. There will be 3 flags in each row.

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Problem 3

A tailor has 33 meters of green ribbon and 15 meters of yellow 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 33 and 15. The GCF of 33 and 15 is 3. The ribbon is 3 meters long.

Explanation

For calculating the longest length of the ribbon first we need to calculate the GCF of 33 and 15 which is 3. The length of each piece of the ribbon will be 3 meters.

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Problem 4

A carpenter has two wooden planks, one 33 cm long and the other 15 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 33 and 15 is 3. The longest length of each piece is 3 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 33 cm and 15 cm, respectively. We have to find the GCF of 33 and 15, which is 3 cm. The longest length of each piece is 3 cm.

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Problem 5

If the GCF of 33 and ‘a’ is 3, and the LCM is 165. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 15.

Explanation

GCF x LCM = product of the numbers 3 × 165 = 33 × a 495 = 33a a = 495 ÷ 33 = 15

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FAQs on the Greatest Common Factor of 33 and 15

1.What is the LCM of 33 and 15?

The LCM of 33 and 15 is 165.

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 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 15?

The prime factorization of 15 is 3 x 5.

5.Are 33 and 15 prime numbers?

No, 33 and 15 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 33 and 15

Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15. 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, 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 33 are 3 and 11. Remainder: The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 15, the remainder is 3 and the quotient is 2. LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 33 and 15 is 165.

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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.