What is the GCF for 14 and 42?

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 14 and 42 would be 14.

What is the highest common multiple of 14 and 42?

LCM of 14 and 42 is 42 and the Highest Common Factor of 14 and 42 is 14.

What is the GCF of 42?

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6, 7, 14, 21, 42. Since 42 is the largest of these common factors, the GCF of 42 and 42 would be 42.

How to calculate GCF?

Here's how to find the GCF of a set of numbers using prime factorization: List the prime factors of each number. Circle every common prime factor — that is, every prime factor that's a factor of every number in the set. Multiply all the circled numbers. The result is the GCF. Jul 9, 2021

Is the LCM of 14 and 42 is 42?

FAQs on LCM of 14 and 42 The LCM of 14 and 42 is 42 . To find the least common multiple (LCM) of 14 and 42, we need to find the multiples of 14 and 42 (multiples of 14 = 14, 28, 42, 56; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 14 and 42, i.e., 42.

What are the multiples of 14 and 42?

Multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420,… Multiples of 14 are 1, 28, 42, 56, 70, 84, 98, 112, 126, 140 ,… The common multiples among the first ten multiples of both the numbers are 42, 84, and 126. There will be infinitely many common multiples of 42 and 14.

The factors of 14 are 1, 2, 7 and 14 .

What are the factors of 42? The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

How to get 42 by multiplying?

In this case 2, 3, 6, and 7 are all numbers you can multiply to get 42. So, they are all factors of 42.

How to find the factors of 14?

Factors of 14 are the numbers obtained when you divide the original number 14 evenly without leaving the remainder. Though the number 14 is composite, it has two factors other than one and the number itself. Factors of 14 are 1, 2, 7, and 14. To find the factors of 14, you need to use the division method.

What is the LCM of 8 and 12?

What is LCM of 8 and 12. The Least Common Multiple or Lowest Common Multiple of 8 and 12 is 24 .

Is 14 a factor of 42?

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42 .

What is the GCF of 44 and 14?

The greatest common factor, or GCF, of 14 and 44 is 2 .

Is 14 a prime factor of 42?

42 is a composite number, thus it has many factors other than one and the number itself. Thus, all the factors 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Amongst these factors 2, 3, and 7 are the only prime factors .

GCF of 14 and 42 | How to Find GCF of 14, 42? (2024)

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.

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

What is GCF of 14 and 42?

Answer: GCF of 14 and 42 is 14.

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.

Methods to Find GCF of 14 and 42

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

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 14 and 42 by Prime Factorization

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 1: Divide 42 (larger number) by 14 (smaller number).
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

Factors of 14: 1, 2, 7, 14
Factors 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.

☛ Also Check:

GCF of 25 and 75 = 25
GCF of 15 and 40 = 5
GCF of 42 and 60 = 6
GCF of 10 and 20 = 10
GCF of 75 and 125 = 25
GCF of 10 and 35 = 5
GCF of 8 and 20 = 4

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.
See Also
Multiples of 6 - Multiples of 6 in the tabular form with examples
Solution:
Given: GCF (z, 42) = 14 and LCM (z, 42) = 42
∵ GCF × LCM = 42 × (z)
⇒ z = (GCF × LCM)/42
⇒ z = (14 × 42)/42
⇒ z = 14
Therefore, 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 = 588/14
Therefore, 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, 14
- Factors 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 Factors
By Long Division
By 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.

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

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