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HCF of 4 and 9

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

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

What is HCF of 4 and 9?

Answer: HCF of 4 and 9 is 1.

Explanation:

The HCF of two non-zero integers, x(4) and y(9), is the highest positive integer m(1) that divides both x(4) and y(9) without any remainder.

Methods to Find HCF of 4 and 9

The methods to find the HCF of 4 and 9 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 4 and 9 by Listing Common Factors

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

Since, 1 is the only common factor between 4 and 9. The highest common factor of 4 and 9 is 1.

HCF of 4 and 9 by Prime Factorization

Prime factorization of 4 and 9 is (2 × 2) and (3 × 3) respectively. As visible, there are no common prime factors between 4 and 9, i.e. they are coprime. Hence, the HCF of 4 and 9 will be 1.

HCF of 4 and 9 by Long Division

HCF of 4 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 9 (larger number) by 4 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 4 and 9.

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HCF of 4 and 9 Examples

Example 1: The product of two numbers is 36. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 36
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 36/1
Therefore, the LCM is 36.
Example 2: Find the highest number that divides 4 and 9 exactly.

Solution:

The highest number that divides 4 and 9 exactly is their highest common factor, i.e. HCF of 4 and 9.
⇒ Factors of 4 and 9:
- Factors of 4 = 1, 2, 4
- Factors of 9 = 1, 3, 9
Therefore, the HCF of 4 and 9 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 36. If one number is 9, find the other number.

Solution:

Given: HCF (y, 9) = 1 and LCM (y, 9) = 36
∵ HCF × LCM = 9 × (y)
⇒ y = (HCF × LCM)/9
⇒ y = (1 × 36)/9
⇒ y = 4
Therefore, the other number is 4.

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FAQs on HCF of 4 and 9

What is the HCF of 4 and 9?

The HCF of 4 and 9 is 1. To calculate the Highest common factor of 4 and 9, we need to factor each number (factors of 4 = 1, 2, 4; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 4 and 9, i.e., 1.

How to Find the HCF of 4 and 9 by Long Division Method?

To find the HCF of 4, 9 using long division method, 9 is divided by 4. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 4 and 9 by Prime Factorization?

To find the HCF of 4 and 9, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 9 = 3 × 3.
⇒ There is no common prime factor for 4 and 9. Hence, HCF (4, 9) = 1.
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 4, 9?

The following equation can be used to express the relation between Least Common Multiple and HCF of 4 and 9, i.e. HCF × LCM = 4 × 9.

If the HCF of 9 and 4 is 1, Find its LCM.

HCF(9, 4) × LCM(9, 4) = 9 × 4
Since the HCF of 9 and 4 = 1
⇒ 1 × LCM(9, 4) = 36
Therefore, LCM = 36
☛ HCF Calculator

What are the Methods to Find HCF of 4 and 9?

There are three commonly used methods to find the HCF of 4 and 9.

By Prime Factorization
By Long Division
By Listing Common Factors

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