HCF of 30 and 105

The HCF of 30 and 105 is 15. The greatest number that divides 30 and 105 exactly and without a remainder is the HCF of these numbers. The factors of 30 and 105 are, respectively, (1, 2, 3, 5, 6, 10, 15) and (1, 3, 5, 7, 15, 21, and 35). The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 30 and 105.

Also read: Highest common factor

What is the HCF of 30 and 105?

The answer to this question is 15. This article shows the HCF of 30 and 105 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 30 and 105?

There are three methods to find the HCF of 30 and 105:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 30 and 105 by Prime Factorisation Method

The prime factorisation of 30 and 105 is given by:

Prime factorisation of 30 = (2 × 3 × 5)

Prime factorisation of 105 = (3 × 5 × 7)

Hence, the HCF of 30 and 105 is 3 × 5 = 15.

HCF (30, 105) = 15

HCF of 30 and 105 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 30 and 105.

HCF of 30 and 105

No further division can be done. 

Hence, HCF (30, 105) = 15

HCF of 30 and 105 by Listing the Factors

To calculate the HCF of 30 and 105 by listing out the common factors, list the factors as shown below:

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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Video Lesson on Properties of HCF and LCM

HCF of 30 and 105 Solved Example

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

We have LCM × HCF = product of numbers

⇒ LCM = Product/HCF = 3150/15

Therefore, the LCM is 210.

Frequently Asked Questions on HCF of 30 and 105

Q1

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 and choose the highest factor that exactly divides both 30 and 105, i.e., 15.
Q2

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

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
Q3

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 Long Division
By Listing Common Factors
By Prime Factorisation
Q4

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
Q5

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.

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