Gcf Of 4 And 14

GCF of 14 and 24

GCF of xiv and 24 is the largest possible number that divides 14 and 24 exactly without any remainder. The factors of 14 and 24 are 1, 2, 7, fourteen and 1, ii, three, 4, six, 8, 12, 24 respectively. In that location are 3 commonly used methods to find the GCF of 14 and 24 - Euclidean algorithm, prime factorization, and long division.

ane.	GCF of xiv and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 24?

Answer: GCF of 14 and 24 is 2.

GCF of 14 and 24

Caption:

The GCF of ii non-zero integers, x(fourteen) and y(24), is the greatest positive integer g(2) that divides both ten(14) and y(24) without any remainder.

Methods to Find GCF of 14 and 24

Let'due south await at the different methods for finding the GCF of xiv and 24.

Prime Factorization Method
Using Euclid's Algorithm
List Mutual Factors

GCF of fourteen and 24 by Prime Factorization

GCF of 14 and 24 by Prime Factorization

Prime factorization of 14 and 24 is (2 × seven) and (2 × two × two × 3) respectively. As visible, 14 and 24 have merely i mutual prime factor i.e. 2. Hence, the GCF of xiv and 24 is 2.

GCF of 14 and 24 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(Ten, Y) = GCF(Y, 10 modern Y)
where X > Y and mod is the modulo operator.

Here 10 = 24 and Y = 14

GCF(24, xiv) = GCF(xiv, 24 modern xiv) = GCF(fourteen, 10)
GCF(14, ten) = GCF(10, 14 mod 10) = GCF(10, iv)
GCF(x, iv) = GCF(four, 10 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(two, four mod 2) = GCF(2, 0)
GCF(2, 0) = two (∵ GCF(10, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 14 and 24 is two.

GCF of 14 and 24 by Listing Mutual Factors

Factors of 14: 1, two, 7, 14
Factors of 24: 1, 2, iii, four, 6, 8, 12, 24

There are 2 common factors of 14 and 24, that are 1 and 2. Therefore, the greatest common factor of 14 and 24 is 2.

☛ Also Bank check:

GCF of 12 and 42 = six
GCF of 60 and seventy = x
GCF of 15 and 45 = 15
GCF of 12 and 24 = 12
GCF of 35 and 45 = v
GCF of v and xv = 5
GCF of 30 and 48 = 6

GCF of xiv and 24 Examples

Example 1: For ii numbers, GCF = 2 and LCM = 168. If ane number is fourteen, find the other number.

Solution:

Given: GCF (10, fourteen) = 2 and LCM (x, 14) = 168
∵ GCF × LCM = 14 × (ten)
⇒ x = (GCF × LCM)/xiv
⇒ x = (ii × 168)/14
⇒ x = 24
Therefore, the other number is 24.
Example 2: Find the greatest number that divides 14 and 24 exactly.

Solution:

The greatest number that divides xiv and 24 exactly is their greatest common cistron, i.due east. GCF of 14 and 24.
⇒ Factors of 14 and 24:
- Factors of xiv = 1, two, 7, 14
- Factors of 24 = 1, ii, 3, 4, vi, 8, 12, 24
Therefore, the GCF of xiv and 24 is 2.
Example 3: Find the GCF of 14 and 24, if their LCM is 168.

Solution:

∵ LCM × GCF = 14 × 24
⇒ GCF(xiv, 24) = (14 × 24)/168 = 2
Therefore, the greatest common factor of xiv and 24 is 2.

get to slidego to slidego to slide

Ready to meet the earth through math'southward eyes?

Math is at the core of everything nosotros do. Enjoy solving existent-globe math problems in alive classes and become an good at everything.

Volume a Gratuitous Trial Class

FAQs on GCF of 14 and 24

What is the GCF of xiv and 24?

The GCF of 14 and 24 is 2 . To summate the greatest mutual gene of xiv and 24, we need to cistron each number (factors of xiv = i, 2, 7, 14; factors of 24 = 1, two, 3, iv, 6, 8, 12, 24) and choose the greatest cistron that exactly divides both 14 and 24, i.e., 2.

If the GCF of 24 and 14 is 2, Find its LCM.

GCF(24, 14) × LCM(24, 14) = 24 × 14
Since the GCF of 24 and xiv = 2
⇒ ii × LCM(24, xiv) = 336
Therefore, LCM = 168
☛ Greatest Common Factor Calculator

How to Find the GCF of 14 and 24 by Long Division Method?

To find the GCF of 14, 24 using long sectionalization method, 24 is divided by 14. The corresponding divisor (two) when rest equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of fourteen, 24?

The following equation can be used to limited the relation between To the lowest degree Common Multiple (LCM) and GCF of 14 and 24, i.e. GCF × LCM = 14 × 24.

What are the Methods to Notice GCF of 14 and 24?

In that location are three unremarkably used methods to find the GCF of 14 and 24.

Past Prime Factorization
By Long Sectionalization
Past Euclidean Algorithm

How to Discover the GCF of 14 and 24 by Prime Factorization?

To find the GCF of 14 and 24, nosotros will find the prime factorization of the given numbers, i.e. xiv = 2 × vii; 24 = 2 × 2 × 2 × 3.
⇒ Since 2 is the only common prime number factor of 14 and 24. Hence, GCF (14, 24) = 2.
☛ What is a Prime?