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GCF of 9 and 10

GCF of 9 and 10 is the largest possible number that divides 9 and 10 exactly without any remainder. The factors of 9 and 10 are 1, 3, 9 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 9 and 10 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 9 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 10?

Answer: GCF of 9 and 10 is 1.

Explanation:

The GCF of two non-zero integers, x(9) and y(10), is the greatest positive integer m(1) that divides both x(9) and y(10) without any remainder.

Methods to Find GCF of 9 and 10

Let's look at the different methods for finding the GCF of 9 and 10.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 9 and 10 by Long Division

GCF of 9 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 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 9 and 10.

GCF of 9 and 10 by Prime Factorization

Prime factorization of 9 and 10 is (3 × 3) and (2 × 5) respectively. As visible, there are no common prime factors between 9 and 10, i.e. they are coprime. Hence, the GCF of 9 and 10 will be 1.

GCF of 9 and 10 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 10: 1, 2, 5, 10

Since, 1 is the only common factor between 9 and 10. The Greatest Common Factor of 9 and 10 is 1.

☛ Also Check:

GCF of 9 and 10 Examples

Example 1: Find the GCF of 9 and 10, if their LCM is 90.

Solution:

∵ LCM × GCF = 9 × 10
⇒ GCF(9, 10) = (9 × 10)/90 = 1
Therefore, the greatest common factor of 9 and 10 is 1.
Example 2: Find the greatest number that divides 9 and 10 exactly.

Solution:

The greatest number that divides 9 and 10 exactly is their greatest common factor, i.e. GCF of 9 and 10.
⇒ Factors of 9 and 10:
- Factors of 9 = 1, 3, 9
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 9 and 10 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 90. If one number is 10, find the other number.

Solution:

Given: GCF (z, 10) = 1 and LCM (z, 10) = 90
∵ GCF × LCM = 10 × (z)
⇒ z = (GCF × LCM)/10
⇒ z = (1 × 90)/10
⇒ z = 9
Therefore, the other number is 9.

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FAQs on GCF of 9 and 10

What is the GCF of 9 and 10?

The GCF of 9 and 10 is 1. To calculate the greatest common factor (GCF) of 9 and 10, we need to factor each number (factors of 9 = 1, 3, 9; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 9 and 10, i.e., 1.

How to Find the GCF of 9 and 10 by Long Division Method?

To find the GCF of 9, 10 using long division method, 10 is divided by 9. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 9, 10?

The following equation can be used to express the relation between Least Common Multiple and GCF of 9 and 10, i.e. GCF × LCM = 9 × 10.

What are the Methods to Find GCF of 9 and 10?

There are three commonly used methods to find the GCF of 9 and 10.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 9 and 10 by Prime Factorization?

To find the GCF of 9 and 10, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 10 = 2 × 5.
⇒ There is no common prime factor for 9 and 10. Hence, GCF (9, 10) = 1.
☛ Prime Numbers

If the GCF of 10 and 9 is 1, Find its LCM.

GCF(10, 9) × LCM(10, 9) = 10 × 9
Since the GCF of 10 and 9 = 1
⇒ 1 × LCM(10, 9) = 90
Therefore, LCM = 90
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