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GCF of 9 and 16

GCF of 9 and 16 is the largest possible number that divides 9 and 16 exactly without any remainder. The factors of 9 and 16 are 1, 3, 9 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the GCF of 9 and 16 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 9 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 16?

Answer: GCF of 9 and 16 is 1.

Explanation:

The GCF of two non-zero integers, x(9) and y(16), is the greatest positive integer m(1) that divides both x(9) and y(16) without any remainder.

Methods to Find GCF of 9 and 16

Let's look at the different methods for finding the GCF of 9 and 16.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 9 and 16 by Long Division

GCF of 9 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (7).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 9 and 16.

GCF of 9 and 16 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 16: 1, 2, 4, 8, 16

Since, 1 is the only common factor between 9 and 16. The Greatest Common Factor of 9 and 16 is 1.

GCF of 9 and 16 by Prime Factorization

Prime factorization of 9 and 16 is (3 × 3) and (2 × 2 × 2 × 2) respectively. As visible, there are no common prime factors between 9 and 16, i.e. they are coprime. Hence, the GCF of 9 and 16 will be 1.

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GCF of 9 and 16 Examples

Example 1: For two numbers, GCF = 1 and LCM = 144. If one number is 9, find the other number.

Solution:

Given: GCF (z, 9) = 1 and LCM (z, 9) = 144
∵ GCF × LCM = 9 × (z)
⇒ z = (GCF × LCM)/9
⇒ z = (1 × 144)/9
⇒ z = 16
Therefore, the other number is 16.
Example 2: Find the GCF of 9 and 16, if their LCM is 144.

Solution:

∵ LCM × GCF = 9 × 16
⇒ GCF(9, 16) = (9 × 16)/144 = 1
Therefore, the greatest common factor of 9 and 16 is 1.
Example 3: Find the greatest number that divides 9 and 16 exactly.

Solution:

The greatest number that divides 9 and 16 exactly is their greatest common factor, i.e. GCF of 9 and 16.
⇒ Factors of 9 and 16:
- Factors of 9 = 1, 3, 9
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the GCF of 9 and 16 is 1.

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FAQs on GCF of 9 and 16

What is the GCF of 9 and 16?

The GCF of 9 and 16 is 1. To calculate the GCF (Greatest Common Factor) of 9 and 16, we need to factor each number (factors of 9 = 1, 3, 9; factors of 16 = 1, 2, 4, 8, 16) and choose the greatest factor that exactly divides both 9 and 16, i.e., 1.

If the GCF of 16 and 9 is 1, Find its LCM.

GCF(16, 9) × LCM(16, 9) = 16 × 9
Since the GCF of 16 and 9 = 1
⇒ 1 × LCM(16, 9) = 144
Therefore, LCM = 144
☛ GCF Calculator

What is the Relation Between LCM and GCF of 9, 16?

The following equation can be used to express the relation between LCM and GCF of 9 and 16, i.e. GCF × LCM = 9 × 16.

How to Find the GCF of 9 and 16 by Long Division Method?

To find the GCF of 9, 16 using long division method, 16 is divided by 9. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 9 and 16 by Prime Factorization?

To find the GCF of 9 and 16, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 16 = 2 × 2 × 2 × 2.
⇒ There is no common prime factor for 9 and 16. Hence, GCF (9, 16) = 1.
☛ What is a Prime Number?

What are the Methods to Find GCF of 9 and 16?

There are three commonly used methods to find the GCF of 9 and 16.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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