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GCF of 7 and 49

GCF of 7 and 49 is the largest possible number that divides 7 and 49 exactly without any remainder. The factors of 7 and 49 are 1, 7 and 1, 7, 49 respectively. There are 3 commonly used methods to find the GCF of 7 and 49 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 7 and 49
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 49?

Answer: GCF of 7 and 49 is 7.

Explanation:

The GCF of two non-zero integers, x(7) and y(49), is the greatest positive integer m(7) that divides both x(7) and y(49) without any remainder.

Methods to Find GCF of 7 and 49

The methods to find the GCF of 7 and 49 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 7 and 49 by Listing Common Factors

Factors of 7: 1, 7
Factors of 49: 1, 7, 49

There are 2 common factors of 7 and 49, that are 1 and 7. Therefore, the greatest common factor of 7 and 49 is 7.

GCF of 7 and 49 by Prime Factorization

Prime factorization of 7 and 49 is (7) and (7 × 7) respectively. As visible, 7 and 49 have only one common prime factor i.e. 7. Hence, the GCF of 7 and 49 is 7.

GCF of 7 and 49 by Long Division

GCF of 7 and 49 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 49 (larger number) by 7 (smaller number).
Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 49.

The corresponding divisor (7) is the GCF of 7 and 49.

☛ Also Check:

GCF of 7 and 49 Examples

Example 1: Find the GCF of 7 and 49, if their LCM is 49.

Solution:

∵ LCM × GCF = 7 × 49
⇒ GCF(7, 49) = (7 × 49)/49 = 7
Therefore, the greatest common factor of 7 and 49 is 7.
Example 2: For two numbers, GCF = 7 and LCM = 49. If one number is 7, find the other number.

Solution:

Given: GCF (x, 7) = 7 and LCM (x, 7) = 49
∵ GCF × LCM = 7 × (x)
⇒ x = (GCF × LCM)/7
⇒ x = (7 × 49)/7
⇒ x = 49
Therefore, the other number is 49.
Example 3: Find the greatest number that divides 7 and 49 exactly.

Solution:

The greatest number that divides 7 and 49 exactly is their greatest common factor, i.e. GCF of 7 and 49.
⇒ Factors of 7 and 49:
- Factors of 7 = 1, 7
- Factors of 49 = 1, 7, 49
Therefore, the GCF of 7 and 49 is 7.

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FAQs on GCF of 7 and 49

What is the GCF of 7 and 49?

The GCF of 7 and 49 is 7. To calculate the GCF of 7 and 49, we need to factor each number (factors of 7 = 1, 7; factors of 49 = 1, 7, 49) and choose the greatest factor that exactly divides both 7 and 49, i.e., 7.

How to Find the GCF of 7 and 49 by Prime Factorization?

To find the GCF of 7 and 49, we will find the prime factorization of the given numbers, i.e. 7 = 7; 49 = 7 × 7.
⇒ Since 7 is the only common prime factor of 7 and 49. Hence, GCF (7, 49) = 7.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 7, 49?

The following equation can be used to express the relation between Least Common Multiple and GCF of 7 and 49, i.e. GCF × LCM = 7 × 49.

If the GCF of 49 and 7 is 7, Find its LCM.

GCF(49, 7) × LCM(49, 7) = 49 × 7
Since the GCF of 49 and 7 = 7
⇒ 7 × LCM(49, 7) = 343
Therefore, LCM = 49
☛ GCF Calculator

What are the Methods to Find GCF of 7 and 49?

There are three commonly used methods to find the GCF of 7 and 49.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 7 and 49 by Long Division Method?

To find the GCF of 7, 49 using long division method, 49 is divided by 7. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

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