GCF of 36 and 42
2026-02-28 10:41 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 42.

What is the GCF of 36 and 42?

The greatest common factor of 36 and 42 is 6. 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 42?

To find the GCF of 36 and 42, a few methods are described below:

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

GCF of 36 and 42 by Using Listing of factors

Steps to find the GCF of 36 and 42 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 42 = 1, 2, 3, 6, 7, 14, 21, 42.

Step 2: Now, identify the common factors of them Common factors of 36 and 42: 1, 2, 3, 6.

Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 36 and 42 is 6.

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GCF of 36 and 42 Using Prime Factorization

To find the GCF of 36 and 42 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 42: 42 = 2 x 3 x 7 = 21 x 31 x 71

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3 = 21 x 31

Step 3: Multiply the common prime factors 21 x 31 = 2 x 3 = 6.

The Greatest Common Factor of 36 and 42 is 6.

GCF of 36 and 42 Using Division Method or Euclidean Algorithm Method

Find the GCF of 36 and 42 using the division method or Euclidean Algorithm Method. Follow these steps:

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

Here, divide 42 by 36 42 ÷ 36 = 1 (quotient).

The remainder is calculated as 42 − (36×1) = 6.

The remainder is 6, not zero, so continue the process

Step 2: Now divide the previous divisor (36) by the previous remainder (6).

Divide 36 by 6 36 ÷ 6 = 6 (quotient), remainder = 36 − (6×6) = 0.

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

The GCF of 36 and 42 is 6.

Common Mistakes and How to Avoid Them in GCF of 36 and 42

Finding GCF of 36 and 42 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 florist has 36 roses and 42 tulips. She wants to group them into equal bouquets, with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?

Okay, lets begin

We should find the GCF of 36 and 42. GCF of 36 and 42 is 6.

There are 6 equal bouquets. 36 ÷ 6 = 6 42 ÷ 6 = 7

There will be 6 bouquets, and each bouquet gets 6 roses and 7 tulips.

Explanation

As the GCF of 36 and 42 is 6, the florist can make 6 bouquets.

Now divide 36 and 42 by 6.

Each bouquet gets 6 roses and 7 tulips.

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Problem 2

A chef has 36 chocolate bars and 42 candy bars. He wants to arrange them on plates with the same number of bars on each plate, using the largest possible number of bars per plate. How many bars will be on each plate?

Okay, lets begin

GCF of 36 and 42 is 6.

So each plate will have 6 bars.

Explanation

There are 36 chocolate bars and 42 candy bars.

To find the total number of bars on each plate, we should find the GCF of 36 and 42.

There will be 6 bars on each plate.

Well explained 👍

Problem 3

A construction worker has 36 meters of steel rod and 42 meters of copper rod. He wants to cut both rods 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 42.

The GCF of 36 and 42 is 6.

The rod is 6 meters long.

Explanation

For calculating the longest length of the rod, first, we need to calculate the GCF of 36 and 42, which is 6. The length of each piece of the rod will be 6 meters.

Well explained 👍

Problem 4

A gardener has two hoses, one 36 meters long and the other 42 meters long. He wants to cut them into the longest possible equal pieces, without any hose left over. What should be the length of each piece?

Okay, lets begin

The gardener needs the longest piece of hose. GCF of 36 and 42 is 6. The longest length of each piece is 6 meters.

Explanation

To find the longest length of each piece of the two hoses, 36 meters and 42 meters, respectively. We have to find the GCF of 36 and 42, which is 6 meters. The longest length of each piece is 6 meters.

Well explained 👍

Problem 5

If the GCF of 36 and ‘b’ is 6, and the LCM is 252. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 42.

Explanation

GCF x LCM = product of the numbers

6 x 252 = 36 x b

1512 = 36b

b = 1512 ÷ 36 = 42

Well explained 👍

FAQs on the Greatest Common Factor of 36 and 42

1.What is the LCM of 36 and 42?

The LCM of 36 and 42 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 42?

The prime factorization of 42 is 2 x 3 x 7.

5.Are 36 and 42 prime numbers?

No, 36 and 42 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 36 and 42

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 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 42 are 2, 3, and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 42 is divided by 6, the remainder is 0 and the quotient is 7.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 42 is 252.

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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.