GCF of 14 and 42 is the largest possible number that divides 14 and 42 exactly without any remainder. The factors of 14 and 42 are 1, 2, 7, 14 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 14 and 42 - Euclidean algorithm, prime factorization, and long division.

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1.GCF of 14 and 42
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 14 and 42 is 14.

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Explanation:

The GCF of two non-zero integers, x(14) and y(42), is the greatest positive integer m(14) that divides both x(14) and y(42) without any remainder.


The methods to find the GCF of 14 and 42 are explained below.

Prime Factorization MethodLong Division MethodListing Common Factors

GCF of 14 and 42 by Prime Factorization

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Prime factorization of 14 and 42 is (2 × 7) and (2 × 3 × 7) respectively. As visible, 14 and 42 have common prime factors. Hence, the GCF of 14 and 42 is 2 × 7 = 14.

GCF of 14 and 42 by Long Division

GCF of 14 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 42.

The corresponding divisor (14) is the GCF of 14 and 42.

GCF of 14 and 42 by Listing Common Factors

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Factors of 14: 1, 2, 7, 14Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 4 common factors of 14 and 42, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 14 and 42 is 14.

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GCF of 14 and 42 Examples


Example 1: For two numbers, GCF = 14 and LCM = 42. If one number is 42, find the other number.

Solution:

Given: GCF (z, 42) = 14 and LCM (z, 42) = 42∵ GCF × LCM = 42 × (z)⇒ z = (GCF × LCM)/42⇒ z = (14 × 42)/42⇒ z = 14Therefore, the other number is 14.


Example 2: The product of two numbers is 588. If their GCF is 14, what is their LCM?

Solution:

Given: GCF = 14 and product of numbers = 588∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 588/14Therefore, the LCM is 42.


Example 3: Find the greatest number that divides 14 and 42 exactly.

Solution:

The greatest number that divides 14 and 42 exactly is their greatest common factor, i.e. GCF of 14 and 42.⇒ Factors of 14 and 42:

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

Therefore, the GCF of 14 and 42 is 14.


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FAQs on GCF of 14 and 42

What is the GCF of 14 and 42?

The GCF of 14 and 42 is 14. To calculate the GCF of 14 and 42, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 14 and 42, i.e., 14.

How to Find the GCF of 14 and 42 by Prime Factorization?

To find the GCF of 14 and 42, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 42 = 2 × 3 × 7.⇒ Since 2, 7 are common terms in the prime factorization of 14 and 42. Hence, GCF(14, 42) = 2 × 7 = 14☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 14, 42?

The following equation can be used to express the relation between LCM and GCF of 14 and 42, i.e. GCF × LCM = 14 × 42.

What are the Methods to Find GCF of 14 and 42?

There are three commonly used methods to find the GCF of 14 and 42.

By Listing Common FactorsBy Long DivisionBy Prime Factorization

How to Find the GCF of 14 and 42 by Long Division Method?

To find the GCF of 14, 42 using long division method, 42 is divided by 14. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

See more: What Is Another Name For The Representative Elements ? Definition Of Representative Element

If the GCF of 42 and 14 is 14, Find its LCM.

GCF(42, 14) × LCM(42, 14) = 42 × 14Since the GCF of 42 and 14 = 14⇒ 14 × LCM(42, 14) = 588Therefore, LCM = 42☛ GCF Calculator