GCF of 14 and 42
2026-02-28 17:54 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 14 and 42.

What is the GCF of 14 and 42?

The greatest common factor of 14 and 42 is 14. 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 14 and 42?

To find the GCF of 14 and 42, a few methods are described below:

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

GCF of 14 and 42 by Using Listing of Factors

Steps to find the GCF of 14 and 42 using the listing of factors:

Step 1: Firstly, list the factors of each number.

Factors of 14 = 1, 2, 7, 14.

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.

Step 2: Now, identify the common factors of them.

Common factors of 14 and 42: 1, 2, 7, 14.

Step 3: Choose the largest factor.

The largest factor that both numbers have is 14.

The GCF of 14 and 42 is 14.

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GCF of 14 and 42 Using Prime Factorization

To find the GCF of 14 and 42 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number:

Prime Factors of 14: 14 = 2 x 7

Prime Factors of 42: 42 = 2 x 3 x 7

Step 2: Now, identify the common prime factors. The common prime factors are: 2 x 7

Step 3: Multiply the common prime factors 2 x 7 = 14.

The Greatest Common Factor of 14 and 42 is 14.

GCF of 14 and 42 Using Division Method or Euclidean Algorithm Method

Find the GCF of 14 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 14 42 ÷ 14 = 3 (quotient), The remainder is calculated as 42 − (14×3) = 0

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

The GCF of 14 and 42 is 14.

Common Mistakes and How to Avoid Them in GCF of 14 and 42

Finding GCF of 14 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 chef has 14 apples and 42 oranges. She wants to create fruit baskets with the largest number of fruits in each basket. How many fruits will be in each basket?

Okay, lets begin

We should find the GCF of 14 and 42 GCF of 14 and 42

2 x 7 = 14.

There are 14 equal groups

14 ÷ 14 = 1

42 ÷ 14 = 3

There will be 14 groups, and each group gets 1 apple and 3 oranges.

Explanation

As the GCF of 14 and 42 is 14, the chef can make 14 groups.

Now divide 14 and 42 by 14.

Each group gets 1 apple and 3 oranges.

Well explained 👍

Problem 2

A school has 14 red chairs and 42 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 14 and 42

2 x 7 = 14.

So each row will have 14 chairs.

Explanation

There are 14 red and 42 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 14 and 42.

There will be 14 chairs in each row.

Well explained 👍

Problem 3

A tailor has 14 meters of red ribbon and 42 meters of blue 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 14 and 42

The GCF of 14 and 42

2 x 7 = 14.

The ribbon is 14 meters long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 14 and 42, which is 14. The length of each piece of the ribbon will be 14 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 14 cm long and the other 42 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 14 and 42

2 x 7 = 14.

The longest length of each piece is 14 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 14 cm and 42 cm, respectively.

We have to find the GCF of 14 and 42, which is 14 cm.

The longest length of each piece is 14 cm.

Well explained 👍

Problem 5

If the GCF of 14 and ‘a’ is 14, and the LCM is 42. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 42.

Explanation

GCF x LCM = product of the numbers

14 × 42 = 14 × a

588 = 14a

a = 588 ÷ 14 = 42

Well explained 👍

FAQs on the Greatest Common Factor of 14 and 42

1.What is the LCM of 14 and 42?

The LCM of 14 and 42 is 42.

2.Is 14 divisible by 2?

Yes, 14 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 42?

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

5.Are 14 and 42 prime numbers?

No, 14 and 42 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 14 and 42

  • 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 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 42 are 2, 3, and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 43 is divided by 7, the remainder is 1 and the quotient is 6.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 42 is 42.

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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.