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.
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
What is the HCF of 30 and 105?
How to Find the HCF of 30 and 105 by Prime Factorisation?
⇒ Since 3, 5 are common terms in the prime factorization of 30 and 105. Hence, HCF(30, 105) = 3 × 5 = 15
What are the Methods to Find HCF of 30 and 105?
By Long Division
By Listing Common Factors
By Prime Factorisation
If the HCF of 105 and 30 is 15, Find its LCM.
Since the HCF of 105 and 30 = 15
⇒ 15 × LCM(105, 30) = 3150
Therefore, LCM = 210
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