28 42
28 42
GCF of 28 and 42
GCF of 28 and 42 is the largest possible number that divides 28 and 42 exactly without any residuum. The factors of 28 and 42 are one, 2, 4, seven, 14, 28 and 1, two, 3, halfdozen, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 28 and 42 – prime factorization, long partitioning, and Euclidean algorithm.
i.  GCF of 28 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 28 and 42?
Respond:
GCF of 28 and 42 is 14.
Explanation:
The GCF of two nonnothing integers, ten(28) and y(42), is the greatest positive integer m(14) that divides both x(28) and y(42) without any residue.
Methods to Find GCF of 28 and 42
The methods to find the GCF of 28 and 42 are explained below.
 List Common Factors
 Long Partition Method
 Prime Factorization Method
GCF of 28 and 42 past Listing Common Factors

Factors of 28:
1, 2, 4, vii, 14, 28 
Factors of 42:
1, two, iii, vi, vii, 14, 21, 42
There are four common factors of 28 and 42, that are ane, 2, xiv, and 7. Therefore, the greatest common factor of 28 and 42 is 14.
GCF of 28 and 42 past Long Division
GCF of 28 and 42 is the divisor that we get when the residual becomes 0 later on doing long sectionalization repeatedly.

Step 1:
Divide 42 (larger number) past 28 (smaller number). 
Footstep two:
Since the remainder ≠ 0, we volition split the divisor of step 1 (28) past the remainder (xiv). 
Step 3:
Repeat this procedure until the remainder = 0.
The corresponding divisor (fourteen) is the GCF of 28 and 42.
GCF of 28 and 42 past Prime Factorization
Prime factorization of 28 and 42 is (2 × 2 × 7) and (2 × iii × seven) respectively. As visible, 28 and 42 have common prime number factors. Hence, the GCF of 28 and 42 is 2 × 7 = 14.
☛ Also Check:
 GCF of 35 and 63 = 7
 GCF of 7 and 14 = 7
 GCF of xiv and 49 = 7
 GCF of 28 and 49 = 7
 GCF of 35 and 50 = v
 GCF of 12 and 14 = 2
 GCF of 26 and 52 = 26
GCF of 28 and 42 Examples

Case 1: For 2 numbers, GCF = xiv and LCM = 84. If one number is 28, notice the other number.
Solution:
Given: GCF (10, 28) = 14 and LCM (x, 28) = 84
∵ GCF × LCM = 28 × (10)
⇒ x = (GCF × LCM)/28
⇒ ten = (fourteen × 84)/28
⇒ x = 42
Therefore, the other number is 42. 
Example 2: Find the GCF of 28 and 42, if their LCM is 84.
Solution:
∵ LCM × GCF = 28 × 42
⇒ GCF(28, 42) = (28 × 42)/84 = fourteen
Therefore, the greatest mutual cistron of 28 and 42 is 14. 
Instance 3: The product of ii numbers is 1176. If their GCF is 14, what is their LCM?
Solution:
Given: GCF = fourteen and production of numbers = 1176
∵ LCM × GCF = production of numbers
⇒ LCM = Production/GCF = 1176/14
Therefore, the LCM is 84.
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FAQs on GCF of 28 and 42
What is the GCF of 28 and 42?
The
GCF of 28 and 42 is fourteen
. To calculate the greatest common cistron (GCF) of 28 and 42, nosotros need to factor each number (factors of 28 = 1, 2, 4, vii, fourteen, 28; factors of 42 = 1, 2, iii, half dozen, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 28 and 42, i.east., xiv.
How to Discover the GCF of 28 and 42 past Long Partition Method?
To find the GCF of 28, 42 using long division method, 42 is divided by 28. The corresponding divisor (xiv) when balance equals 0 is taken as GCF.
If the GCF of 42 and 28 is fourteen, Observe its LCM.
GCF(42, 28) × LCM(42, 28) = 42 × 28
Since the GCF of 42 and 28 = 14
⇒ 14 × LCM(42, 28) = 1176
Therefore, LCM = 84
☛ Greatest Mutual Factor Calculator
What is the Relation Between LCM and GCF of 28, 42?
The following equation tin can be used to express the relation betwixt LCM (To the lowest degree Common Multiple) and GCF of 28 and 42, i.e. GCF × LCM = 28 × 42.
How to Observe the GCF of 28 and 42 by Prime Factorization?
To find the GCF of 28 and 42, nosotros will detect the prime factorization of the given numbers, i.due east. 28 = ii × 2 × 7; 42 = ii × 3 × vii.
⇒ Since ii, 7 are common terms in the prime factorization of 28 and 42. Hence, GCF(28, 42) = two × 7 = 14
☛ Prime number Number
What are the Methods to Find GCF of 28 and 42?
There are three commonly used methods to notice the
GCF of 28 and 42.
 By Listing Common Factors
 Past Prime number Factorization
 By Long Partitioning
28 42
Source: https://www.cuemath.com/numbers/gcfof28and42/