Factors Of 42 And 12

GCF of 12 and 42

GCF of 12 and 42 is the largest possible number that divides 12 and 42 exactly without whatever remainder. The factors of 12 and 42 are 1, 2, iii, four, 6, 12 and ane, two, 3, 6, 7, 14, 21, 42 respectively. At that place are 3 commonly used methods to find the GCF of 12 and 42 - prime number factorization, Euclidean algorithm, and long partition.

1.	GCF of 12 and 42
2.	List of Methods
3.	Solved Examples
iv.	FAQs

What is GCF of 12 and 42?

Answer: GCF of 12 and 42 is six.

GCF of 12 and 42

Explanation:

The GCF of two non-zilch integers, ten(12) and y(42), is the greatest positive integer m(6) that divides both ten(12) and y(42) without whatever residuum.

Methods to Discover GCF of 12 and 42

Allow'due south wait at the dissimilar methods for finding the GCF of 12 and 42.

List Mutual Factors
Prime number Factorization Method
Using Euclid's Algorithm

GCF of 12 and 42 by List Common Factors

GCF of 12 and 42 by Listing Common Factors

Factors of 12: i, 2, 3, 4, 6, 12
Factors of 42: 1, 2, 3, half-dozen, 7, 14, 21, 42

There are 4 common factors of 12 and 42, that are 1, 2, 3, and six. Therefore, the greatest mutual factor of 12 and 42 is six.

GCF of 12 and 42 by Prime Factorization

Prime factorization of 12 and 42 is (2 × 2 × 3) and (two × three × vii) respectively. Every bit visible, 12 and 42 have common prime factors. Hence, the GCF of 12 and 42 is ii × three = six.

GCF of 12 and 42 by Euclidean Algorithm

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

Hither 10 = 42 and Y = 12

GCF(42, 12) = GCF(12, 42 modernistic 12) = GCF(12, six)
GCF(12, vi) = GCF(6, 12 modernistic vi) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(10, 0) = |X|, where Ten ≠ 0)

Therefore, the value of GCF of 12 and 42 is vi.

☛ Also Bank check:

GCF of 72 and fourscore = viii
GCF of 63 and 54 = 9
GCF of 20 and 32 = 4
GCF of six and 21 = three
GCF of seven and eight = one
GCF of 9 and 30 = 3
GCF of 12 and xiii = 1

GCF of 12 and 42 Examples

Example one: The product of two numbers is 504. If their GCF is vi, what is their LCM?

Solution:

Given: GCF = half-dozen and product of numbers = 504
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 504/6
Therefore, the LCM is 84.
Example two: Detect the greatest number that divides 12 and 42 exactly.

Solution:

The greatest number that divides 12 and 42 exactly is their greatest common gene, i.e. GCF of 12 and 42.
⇒ Factors of 12 and 42:
- Factors of 12 = 1, two, three, 4, 6, 12
- Factors of 42 = 1, 2, 3, 6, seven, 14, 21, 42
Therefore, the GCF of 12 and 42 is 6.
Case iii: For two numbers, GCF = half-dozen and LCM = 84. If i number is 12, notice the other number.

Solution:

Given: GCF (y, 12) = 6 and LCM (y, 12) = 84
∵ GCF × LCM = 12 × (y)
⇒ y = (GCF × LCM)/12
⇒ y = (6 × 84)/12
⇒ y = 42
Therefore, the other number is 42.

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FAQs on GCF of 12 and 42

What is the GCF of 12 and 42?

The GCF of 12 and 42 is 6 . To calculate the greatest common factor (GCF) of 12 and 42, we need to factor each number (factors of 12 = 1, 2, iii, iv, half-dozen, 12; factors of 42 = 1, 2, 3, vi, seven, xiv, 21, 42) and choose the greatest factor that exactly divides both 12 and 42, i.e., 6.

If the GCF of 42 and 12 is 6, Find its LCM.

GCF(42, 12) × LCM(42, 12) = 42 × 12
Since the GCF of 42 and 12 = half-dozen
⇒ vi × LCM(42, 12) = 504
Therefore, LCM = 84
☛ Greatest Mutual Factor Computer

How to Discover the GCF of 12 and 42 by Long Division Method?

To detect the GCF of 12, 42 using long division method, 42 is divided by 12. The corresponding divisor (half dozen) when remainder equals 0 is taken equally GCF.

What are the Methods to Find GCF of 12 and 42?

There are three normally used methods to detect the GCF of 12 and 42.

By Long Division
By Prime Factorization
Past Listing Common Factors

How to Notice the GCF of 12 and 42 past Prime Factorization?

To find the GCF of 12 and 42, we will observe the prime factorization of the given numbers, i.e. 12 = 2 × two × 3; 42 = 2 × 3 × vii.
⇒ Since 2, 3 are common terms in the prime number factorization of 12 and 42. Hence, GCF(12, 42) = 2 × 3 = 6
☛ Prime

What is the Relation Between LCM and GCF of 12, 42?

The post-obit equation can be used to express the relation between LCM and GCF of 12 and 42, i.eastward. GCF × LCM = 12 × 42.