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GCF of 7 and 10

GCF of 7 and 10 is the largest possible number that divides 7 and 10 exactly without any remainder. The factors of 7 and 10 are 1, 7 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 7 and 10 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 7 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 10?

Answer: GCF of 7 and 10 is 1.

Explanation:

The GCF of two non-zero integers, x(7) and y(10), is the greatest positive integer m(1) that divides both x(7) and y(10) without any remainder.

Methods to Find GCF of 7 and 10

The methods to find the GCF of 7 and 10 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 7 and 10 by Long Division

GCF of 7 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10 (larger number) by 7 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 7 and 10.

GCF of 7 and 10 by Listing Common Factors

Factors of 7: 1, 7
Factors of 10: 1, 2, 5, 10

Since, 1 is the only common factor between 7 and 10. The Greatest Common Factor of 7 and 10 is 1.

GCF of 7 and 10 by Prime Factorization

Prime factorization of 7 and 10 is (7) and (2 × 5) respectively. As visible, there are no common prime factors between 7 and 10, i.e. they are coprime. Hence, the GCF of 7 and 10 will be 1.

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GCF of 7 and 10 Examples

Example 1: The product of two numbers is 70. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 70
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 70/1
Therefore, the LCM is 70.
Example 2: For two numbers, GCF = 1 and LCM = 70. If one number is 7, find the other number.

Solution:

Given: GCF (z, 7) = 1 and LCM (z, 7) = 70
∵ GCF × LCM = 7 × (z)
⇒ z = (GCF × LCM)/7
⇒ z = (1 × 70)/7
⇒ z = 10
Therefore, the other number is 10.
Example 3: Find the greatest number that divides 7 and 10 exactly.

Solution:

The greatest number that divides 7 and 10 exactly is their greatest common factor, i.e. GCF of 7 and 10.
⇒ Factors of 7 and 10:
- Factors of 7 = 1, 7
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 7 and 10 is 1.

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FAQs on GCF of 7 and 10

What is the GCF of 7 and 10?

The GCF of 7 and 10 is 1. To calculate the greatest common factor of 7 and 10, we need to factor each number (factors of 7 = 1, 7; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 7 and 10, i.e., 1.

What is the Relation Between LCM and GCF of 7, 10?

The following equation can be used to express the relation between LCM and GCF of 7 and 10, i.e. GCF × LCM = 7 × 10.

How to Find the GCF of 7 and 10 by Long Division Method?

To find the GCF of 7, 10 using long division method, 10 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 7 and 10 by Prime Factorization?

To find the GCF of 7 and 10, we will find the prime factorization of the given numbers, i.e. 7 = 7; 10 = 2 × 5.
⇒ There is no common prime factor for 7 and 10. Hence, GCF (7, 10) = 1.
☛ Prime Numbers

What are the Methods to Find GCF of 7 and 10?

There are three commonly used methods to find the GCF of 7 and 10.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 10 and 7 is 1, Find its LCM.

GCF(10, 7) × LCM(10, 7) = 10 × 7
Since the GCF of 10 and 7 = 1
⇒ 1 × LCM(10, 7) = 70
Therefore, LCM = 70
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