Gcf Of 28 And 14
GCF of xiv and 28
GCF of fourteen and 28 is the largest possible number that divides 14 and 28 exactly without any rest. The factors of xiv and 28 are 1, 2, 7, xiv and 1, 2, iv, 7, 14, 28 respectively. There are 3 normally used methods to find the GCF of 14 and 28 - long division, Euclidean algorithm, and prime factorization.
| ane. | GCF of 14 and 28 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of fourteen and 28?
Answer: GCF of 14 and 28 is 14.
Explanation:
The GCF of 2 not-goose egg integers, 10(14) and y(28), is the greatest positive integer m(14) that divides both 10(14) and y(28) without whatever residual.
Methods to Observe GCF of 14 and 28
The methods to discover the GCF of 14 and 28 are explained below.
- Using Euclid's Algorithm
- Long Partition Method
- Prime number Factorization Method
GCF of fourteen and 28 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and modern is the modulo operator.
Here X = 28 and Y = 14
- GCF(28, 14) = GCF(14, 28 modern 14) = GCF(fourteen, 0)
- GCF(14, 0) = fourteen (∵ GCF(Ten, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 14 and 28 is 14.
GCF of 14 and 28 by Long Division
GCF of 14 and 28 is the divisor that nosotros go when the remainder becomes 0 after doing long division repeatedly.
- Footstep 1: Separate 28 (larger number) by 14 (smaller number).
- Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 28.
The corresponding divisor (fourteen) is the GCF of 14 and 28.
GCF of 14 and 28 by Prime Factorization
Prime factorization of 14 and 28 is (2 × 7) and (2 × ii × 7) respectively. As visible, fourteen and 28 accept common prime factors. Hence, the GCF of 14 and 28 is two × 7 = fourteen.
☛ Also Check:
- GCF of 48 and 72 = 24
- GCF of 24 and 28 = 4
- GCF of 16 and 32 = 16
- GCF of 12 and 20 = iv
- GCF of 175 and 25 = 25
- GCF of 32 and 81 = 1
- GCF of 33 and 66 = 33
GCF of 14 and 28 Examples
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FAQs on GCF of fourteen and 28
What is the GCF of 14 and 28?
The GCF of 14 and 28 is fourteen . To summate the GCF of fourteen and 28, nosotros need to cistron each number (factors of 14 = 1, 2, 7, xiv; factors of 28 = ane, two, 4, 7, 14, 28) and choose the greatest factor that exactly divides both xiv and 28, i.eastward., 14.
What are the Methods to Find GCF of 14 and 28?
There are three unremarkably used methods to notice the GCF of xiv and 28.
- By Prime Factorization
- Past Long Division
- By Listing Common Factors
If the GCF of 28 and 14 is 14, Find its LCM.
GCF(28, 14) × LCM(28, xiv) = 28 × 14
Since the GCF of 28 and 14 = 14
⇒ 14 × LCM(28, 14) = 392
Therefore, LCM = 28
☛ GCF Estimator
How to Find the GCF of 14 and 28 by Prime Factorization?
To find the GCF of 14 and 28, nosotros will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 28 = 2 × ii × 7.
⇒ Since 2, 7 are common terms in the prime number factorization of 14 and 28. Hence, GCF(fourteen, 28) = 2 × 7 = xiv
☛ What are Prime Numbers?
What is the Relation Betwixt LCM and GCF of fourteen, 28?
The following equation tin exist used to express the relation between Least Mutual Multiple and GCF of xiv and 28, i.east. GCF × LCM = 14 × 28.
How to Observe the GCF of 14 and 28 by Long Division Method?
To detect the GCF of 14, 28 using long partitioning method, 28 is divided past 14. The corresponding divisor (14) when residue equals 0 is taken equally GCF.
Gcf Of 28 And 14,
Source: https://www.cuemath.com/numbers/gcf-of-14-and-28/
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