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GCF of 14 and 35

GCF of 14 and 35 is the largest possible number that divides 14 and 35 exactly without any remainder. The factors of 14 and 35 are 1, 2, 7, 14 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 14 and 35 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 14 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 35?

Answer: GCF of 14 and 35 is 7.

Explanation:

The GCF of two non-zero integers, x(14) and y(35), is the greatest positive integer m(7) that divides both x(14) and y(35) without any remainder.

Methods to Find GCF of 14 and 35

The methods to find the GCF of 14 and 35 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 14 and 35 by Prime Factorization

Prime factorization of 14 and 35 is (2 × 7) and (5 × 7) respectively. As visible, 14 and 35 have only one common prime factor i.e. 7. Hence, the GCF of 14 and 35 is 7.

GCF of 14 and 35 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 14 and 35, that are 1 and 7. Therefore, the greatest common factor of 14 and 35 is 7.

GCF of 14 and 35 by Long Division

GCF of 14 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 14 and 35.

☛ Also Check:

GCF of 14 and 35 Examples

Example 1: Find the GCF of 14 and 35, if their LCM is 70.

Solution:

∵ LCM × GCF = 14 × 35
⇒ GCF(14, 35) = (14 × 35)/70 = 7
Therefore, the greatest common factor of 14 and 35 is 7.
Example 2: For two numbers, GCF = 7 and LCM = 70. If one number is 35, find the other number.

Solution:

Given: GCF (z, 35) = 7 and LCM (z, 35) = 70
∵ GCF × LCM = 35 × (z)
⇒ z = (GCF × LCM)/35
⇒ z = (7 × 70)/35
⇒ z = 14
Therefore, the other number is 14.
Example 3: The product of two numbers is 490. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 490
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 490/7
Therefore, the LCM is 70.

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FAQs on GCF of 14 and 35

What is the GCF of 14 and 35?

The GCF of 14 and 35 is 7. To calculate the GCF (Greatest Common Factor) of 14 and 35, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 14 and 35, i.e., 7.

If the GCF of 35 and 14 is 7, Find its LCM.

GCF(35, 14) × LCM(35, 14) = 35 × 14
Since the GCF of 35 and 14 = 7
⇒ 7 × LCM(35, 14) = 490
Therefore, LCM = 70
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 14 and 35?

There are three commonly used methods to find the GCF of 14 and 35.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 14 and 35 by Long Division Method?

To find the GCF of 14, 35 using long division method, 35 is divided by 14. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

How to Find the GCF of 14 and 35 by Prime Factorization?

To find the GCF of 14 and 35, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 35 = 5 × 7.
⇒ Since 7 is the only common prime factor of 14 and 35. Hence, GCF (14, 35) = 7.
☛ Prime Number

What is the Relation Between LCM and GCF of 14, 35?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 35, i.e. GCF × LCM = 14 × 35.

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