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GCF of 7 and 35

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

1.	GCF of 7 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 35?

Answer: GCF of 7 and 35 is 7.

Explanation:

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

Methods to Find GCF of 7 and 35

The methods to find the GCF of 7 and 35 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 7 and 35 by Listing Common Factors

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

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

GCF of 7 and 35 by Long Division

GCF of 7 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 7 (smaller number).
Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 35.

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

GCF of 7 and 35 by Prime Factorization

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

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GCF of 7 and 35 Examples

Example 1: For two numbers, GCF = 7 and LCM = 35. If one number is 7, find the other number.

Solution:

Given: GCF (x, 7) = 7 and LCM (x, 7) = 35
∵ GCF × LCM = 7 × (x)
⇒ x = (GCF × LCM)/7
⇒ x = (7 × 35)/7
⇒ x = 35
Therefore, the other number is 35.
Example 2: Find the GCF of 7 and 35, if their LCM is 35.

Solution:

∵ LCM × GCF = 7 × 35
⇒ GCF(7, 35) = (7 × 35)/35 = 7
Therefore, the greatest common factor of 7 and 35 is 7.
Example 3: Find the greatest number that divides 7 and 35 exactly.

Solution:

The greatest number that divides 7 and 35 exactly is their greatest common factor, i.e. GCF of 7 and 35.
⇒ Factors of 7 and 35:
- Factors of 7 = 1, 7
- Factors of 35 = 1, 5, 7, 35
Therefore, the GCF of 7 and 35 is 7.

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FAQs on GCF of 7 and 35

What is the GCF of 7 and 35?

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

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

GCF(35, 7) × LCM(35, 7) = 35 × 7
Since the GCF of 35 and 7 = 7
⇒ 7 × LCM(35, 7) = 245
Therefore, LCM = 35
☛ Greatest Common Factor Calculator

How to Find the GCF of 7 and 35 by Long Division Method?

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

What is the Relation Between LCM and GCF of 7, 35?

The following equation can be used to express the relation between Least Common Multiple and GCF of 7 and 35, i.e. GCF × LCM = 7 × 35.

How to Find the GCF of 7 and 35 by Prime Factorization?

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

What are the Methods to Find GCF of 7 and 35?

There are three commonly used methods to find the GCF of 7 and 35.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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