GCF of 33 and 77
2026-02-21 20:34 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 items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 33 and 77.

What is the GCF of 33 and 77?

The greatest common factor of 33 and 77 is 11. 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 77?

To find the GCF of 33 and 77, a few methods are described below -

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

GCF of 33 and 77 by Using Listing of factors

Steps to find the GCF of 33 and 77 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 33 = 1, 3, 11, 33.

Factors of 77 = 1, 7, 11, 77.

Step 2: Now, identify the common factors of them Common factors of 33 and 77: 1, 11.

Step 3: Choose the largest factor

The largest factor that both numbers have is 11.

The GCF of 33 and 77 is 11.

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GCF of 33 and 77 Using Prime Factorization

To find the GCF of 33 and 77 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 77: 77 = 7 x 11

Step 2: Now, identify the common prime factors

The common prime factor is: 11

Step 3: Multiply the common prime factors 11 = 11.

The Greatest Common Factor of 33 and 77 is 11.

GCF of 33 and 77 Using Division Method or Euclidean Algorithm Method

Find the GCF of 33 and 77 using the division method or Euclidean Algorithm Method. Follow these steps:

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

Here, divide 77 by 33 77 ÷ 33 = 2 (quotient),

The remainder is calculated as 77 − (33×2) = 11

The remainder is 11, not zero, so continue the process

Step 2: Now divide the previous divisor (33) by the previous remainder (11)

Divide 33 by 11 33 ÷ 11 = 3 (quotient), remainder = 33 − (11×3) = 0

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

The GCF of 33 and 77 is 11.

Common Mistakes and How to Avoid Them in GCF of 33 and 77

Finding GCF of 33 and 77 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 farmer has 33 apple trees and 77 orange trees. He wants to arrange them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?

Okay, lets begin

We should find the GCF of 33 and 77

GCF of 33 and 77 11

There are 11 equal groups 33 ÷ 11 = 3 77 ÷ 11 = 7

There will be 11 rows, and each row gets 3 apple trees and 7 orange trees.

Explanation

As the GCF of 33 and 77 is 11, the farmer can make 11 rows. Now divide 33 and 77 by 11. Each row gets 3 apple trees and 7 orange trees.

Well explained 👍

Problem 2

A school has 33 desks and 77 chairs. They want to arrange them in groups with the same number of items in each group, using the largest possible number of items per group. How many items will be in each group?

Okay, lets begin

GCF of 33 and 77 11

So each group will have 11 items.

Explanation

There are 33 desks and 77 chairs. To find the total number of items in each group, we should find the GCF of 33 and 77. There will be 11 items in each group.

Well explained 👍

Problem 3

A tailor has 33 meters of silk and 77 meters of cotton fabric. She wants to cut both fabrics 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 77

The GCF of 33 and 77 11

The fabric is 11 meters long.

Explanation

For calculating the longest length of the fabric, first we need to calculate the GCF of 33 and 77, which is 11. The length of each piece of the fabric will be 11 meters.

Well explained 👍

Problem 4

A carpenter has two wooden beams, one 33 cm long and the other 77 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 77 11

The longest length of each piece is 11 cm.

Explanation

To find the longest length of each piece of the two wooden beams, 33 cm and 77 cm, respectively, we have to find the GCF of 33 and 77, which is 11 cm. The longest length of each piece is 11 cm.

Well explained 👍

Problem 5

If the GCF of 33 and ‘b’ is 11, and the LCM is 231. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 77.

Explanation

GCF x LCM = product of the numbers 11 × 231 = 33 × b

2541 = 33b

b = 2541 ÷ 33 = 77

Well explained 👍

FAQs on the Greatest Common Factor of 33 and 77

1.What is the LCM of 33 and 77?

The LCM of 33 and 77 is 231.

2.Is 33 divisible by 3?

Yes, 33 is divisible by 3 because the sum of its digits (3 + 3) is 6, 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 77?

The prime factorization of 77 is 7 x 11.

5.Are 33 and 77 prime numbers?

No, 33 and 77 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 33 and 77

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 33 are 1, 3, 11, and 33.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 77 are 7 and 11.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 8, the remainder is 1 and the quotient is 4.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 33 and 77 is 231.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 33 and 77 will be 11, 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.