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HCF of 45 and 30

HCF of 45 and 30 is the largest possible number that divides 45 and 30 exactly without any remainder. The factors of 45 and 30 are 1, 3, 5, 9, 15, 45 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the HCF of 45 and 30 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 45 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 45 and 30?

Answer: HCF of 45 and 30 is 15.

Explanation:

The HCF of two non-zero integers, x(45) and y(30), is the highest positive integer m(15) that divides both x(45) and y(30) without any remainder.

Methods to Find HCF of 45 and 30

Let's look at the different methods for finding the HCF of 45 and 30.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 45 and 30 by Prime Factorization

Prime factorization of 45 and 30 is (3 × 3 × 5) and (2 × 3 × 5) respectively. As visible, 45 and 30 have common prime factors. Hence, the HCF of 45 and 30 is 3 × 5 = 15.

HCF of 45 and 30 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 45 and 30, that are 1, 3, 5, and 15. Therefore, the highest common factor of 45 and 30 is 15.

HCF of 45 and 30 by Long Division

HCF of 45 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the HCF of 45 and 30.

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HCF of 45 and 30 Examples

Example 1: Find the highest number that divides 45 and 30 exactly.

Solution:

The highest number that divides 45 and 30 exactly is their highest common factor, i.e. HCF of 45 and 30.
⇒ Factors of 45 and 30:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the HCF of 45 and 30 is 15.
Example 2: Find the HCF of 45 and 30, if their LCM is 90.

Solution:

∵ LCM × HCF = 45 × 30
⇒ HCF(45, 30) = (45 × 30)/90 = 15
Therefore, the highest common factor of 45 and 30 is 15.
Example 3: For two numbers, HCF = 15 and LCM = 90. If one number is 30, find the other number.

Solution:

Given: HCF (x, 30) = 15 and LCM (x, 30) = 90
∵ HCF × LCM = 30 × (x)
⇒ x = (HCF × LCM)/30
⇒ x = (15 × 90)/30
⇒ x = 45
Therefore, the other number is 45.

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FAQs on HCF of 45 and 30

What is the HCF of 45 and 30?

The HCF of 45 and 30 is 15. To calculate the HCF (Highest Common Factor) of 45 and 30, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides both 45 and 30, i.e., 15.

How to Find the HCF of 45 and 30 by Long Division Method?

To find the HCF of 45, 30 using long division method, 45 is divided by 30. The corresponding divisor (15) when remainder equals 0 is taken as HCF.

If the HCF of 30 and 45 is 15, Find its LCM.

HCF(30, 45) × LCM(30, 45) = 30 × 45
Since the HCF of 30 and 45 = 15
⇒ 15 × LCM(30, 45) = 1350
Therefore, LCM = 90
☛ HCF Calculator

What are the Methods to Find HCF of 45 and 30?

There are three commonly used methods to find the HCF of 45 and 30.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the HCF of 45 and 30 by Prime Factorization?

To find the HCF of 45 and 30, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 30 = 2 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 45 and 30. Hence, HCF(45, 30) = 3 × 5 = 15
☛ Prime Number

What is the Relation Between LCM and HCF of 45, 30?

The following equation can be used to express the relation between LCM and HCF of 45 and 30, i.e. HCF × LCM = 45 × 30.

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