GCF of 42 and 64
2026-02-28 23:38 Diff
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Last updated on September 25, 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 42 and 64.

What is the GCF of 42 and 64?

The greatest common factor of 42 and 64 is 2. 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 42 and 64?

To find the GCF of 42 and 64, a few methods are described below

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

GCF of 42 and 64 by Using Listing of Factors

Steps to find the GCF of 42 and 64 using the listing of factors

Step 1: Firstly, list the factors of each number Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42. Factors of 64 = 1, 2, 4, 8, 16, 32, 64.

Step 2: Now, identify the common factors of them Common factors of 42 and 64: 1, 2.

Step 3: Choose the largest factor The largest factor that both numbers have is 2. The GCF of 42 and 64 is 2.

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GCF of 42 and 64 Using Prime Factorization

To find the GCF of 42 and 64 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime factors of 42: 42 = 2 × 3 × 7 Prime factors of 64: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2^6

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

Step 3: Multiply the common prime factors Since 2 is the only common prime factor, the GCF is 2. The Greatest Common Factor of 42 and 64 is 2.

GCF of 42 and 64 Using Division Method or Euclidean Algorithm Method

Find the GCF of 42 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 64 by 42 64 ÷ 42 = 1 (quotient), The remainder is calculated as 64 − (42×1) = 22 The remainder is 22, not zero, so continue the process

Step 2: Now divide the previous divisor (42) by the previous remainder (22) Divide 42 by 22 42 ÷ 22 = 1 (quotient), remainder = 42 − (22×1) = 20

Step 3: Continue the process Divide 22 by 20 22 ÷ 20 = 1 (quotient), remainder = 22 − (20×1) = 2

Step 4: Now divide the previous divisor (20) by the previous remainder (2) Divide 20 by 2 20 ÷ 2 = 10 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF.

The GCF of 42 and 64 is 2.

Common Mistakes and How to Avoid Them in GCF of 42 and 64

Finding the GCF of 42 and 64 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A gardener has 42 rose bushes and 64 tulip bulbs. She wants to plant them in equal rows, with the largest number of plants in each row. How many plants will be in each row?

Okay, lets begin

We should find the GCF of 42 and 64 GCF of 42 and 64 is 2. 42 ÷ 2 = 21 64 ÷ 2 = 32 There will be 2 plants in each row.

Explanation

As the GCF of 42 and 64 is 2, the gardener can plant 2 plants per row.

Now divide 42 and 64 by 2.

Each row has 21 rose bushes and 32 tulip bulbs.

Well explained 👍

Problem 2

A school has 42 yellow desks and 64 blue desks. They want to arrange them in rows with the same number of desks in each row, using the largest possible number of desks per row. How many desks will be in each row?

Okay, lets begin

GCF of 42 and 64 is 2. So each row will have 2 desks.

Explanation

There are 42 yellow and 64 blue desks.

To find the total number of desks in each row, we should find the GCF of 42 and 64.

There will be 2 desks in each row.

Well explained 👍

Problem 3

A tailor has 42 meters of green fabric and 64 meters of yellow 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 42 and 64 The GCF of 42 and 64 is 2. Each piece of fabric will be 2 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 42 and 64, which is 2.

The length of each piece of fabric will be 2 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 42 cm long and the other 64 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 42 and 64 is 2. The longest length of each piece is 2 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 42 cm and 64 cm, respectively.

We have to find the GCF of 42 and 64, which is 2 cm.

The longest length of each piece is 2 cm.

Well explained 👍

Problem 5

If the GCF of 42 and ‘b’ is 2, and the LCM is 1344, find ‘b’.

Okay, lets begin

The value of ‘b’ is 64.

Explanation

GCF × LCM = product of the numbers

2 × 1344 = 42 × b

2688 = 42b

b = 2688 ÷ 42

= 64

Well explained 👍

FAQs on the Greatest Common Factor of 42 and 64

1.What is the LCM of 42 and 64?

The LCM of 42 and 64 is 1344.

2.Is 42 divisible by 2?

Yes, 42 is divisible by 2 because it is an even number.

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 64?

The prime factorization of 64 is 2^6.

5.Are 42 and 64 prime numbers?

No, 42 and 64 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 42 and 64

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
  • 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 28 are 2 and 7.
  • 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 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.

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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.