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HCF of 30 and 105

HCF of 30 and 105 is the largest possible number that divides 30 and 105 exactly without any remainder. The factors of 30 and 105 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 3, 5, 7, 15, 21, 35, 105 respectively. There are 3 commonly used methods to find the HCF of 30 and 105 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 30 and 105
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 30 and 105?

Answer: HCF of 30 and 105 is 15.

Explanation:

The HCF of two non-zero integers, x(30) and y(105), is the highest positive integer m(15) that divides both x(30) and y(105) without any remainder.

Methods to Find HCF of 30 and 105

Let's look at the different methods for finding the HCF of 30 and 105.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 30 and 105 by Prime Factorization

Prime factorization of 30 and 105 is (2 × 3 × 5) and (3 × 5 × 7) respectively. As visible, 30 and 105 have common prime factors. Hence, the HCF of 30 and 105 is 3 × 5 = 15.

HCF of 30 and 105 by Long Division

HCF of 30 and 105 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 105 (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 30 and 105.

HCF of 30 and 105 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

There are 4 common factors of 30 and 105, that are 1, 3, 5, and 15. Therefore, the highest common factor of 30 and 105 is 15.

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HCF of 30 and 105 Examples

Example 1: The product of two numbers is 3150. If their HCF is 15, what is their LCM?

Solution:

Given: HCF = 15 and product of numbers = 3150
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3150/15
Therefore, the LCM is 210.
Example 2: Find the HCF of 30 and 105, if their LCM is 210.

Solution:

∵ LCM × HCF = 30 × 105
⇒ HCF(30, 105) = (30 × 105)/210 = 15
Therefore, the highest common factor of 30 and 105 is 15.
Example 3: For two numbers, HCF = 15 and LCM = 210. If one number is 30, find the other number.

Solution:

Given: HCF (x, 30) = 15 and LCM (x, 30) = 210
∵ HCF × LCM = 30 × (x)
⇒ x = (HCF × LCM)/30
⇒ x = (15 × 210)/30
⇒ x = 105
Therefore, the other number is 105.

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FAQs on HCF of 30 and 105

What is the HCF of 30 and 105?

The HCF of 30 and 105 is 15. To calculate the HCF (Highest Common Factor) of 30 and 105, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105) and choose the highest factor that exactly divides both 30 and 105, i.e., 15.

How to Find the HCF of 30 and 105 by Prime Factorization?

To find the HCF of 30 and 105, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 105 = 3 × 5 × 7.
⇒ Since 3, 5 are common terms in the prime factorization of 30 and 105. Hence, HCF(30, 105) = 3 × 5 = 15
☛ What is a Prime Number?

What are the Methods to Find HCF of 30 and 105?

There are three commonly used methods to find the HCF of 30 and 105.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the HCF of 105 and 30 is 15, Find its LCM.

HCF(105, 30) × LCM(105, 30) = 105 × 30
Since the HCF of 105 and 30 = 15
⇒ 15 × LCM(105, 30) = 3150
Therefore, LCM = 210
☛ Highest Common Factor Calculator

How to Find the HCF of 30 and 105 by Long Division Method?

To find the HCF of 30, 105 using long division method, 105 is divided by 30. The corresponding divisor (15) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 30, 105?

The following equation can be used to express the relation between Least Common Multiple and HCF of 30 and 105, i.e. HCF × LCM = 30 × 105.

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