The HCF of 45 and 30 is 15. The greatest number that divides 45 and 30 perfectly without leaving any residue is the HCF of 45 and 30. 45 and 30 have the factors 1, 3, 5, 9, 15, 45 and 1, 2, 3, 5, 6, 10, 15, 30, respectively. The listing common factors, prime factorisation, and long division are the three regularly used methods to calculate the HCF of 45 and 30.
Also read: Highest common factor
What is the HCF of 45 and 30?
The answer to this question is 15. This article shows the HCF of 45 and 30 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 45 and 30?
There are three methods to find the HCF of 45 and 30:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 45 and 30 by Prime Factorisation Method
The prime factorisation of 45 and 30 is given by:
Prime factorisation of 45 = (3 × 3 × 5)
Prime factorisation of 30 = (2 × 3 × 5)
Common prime factors of 45 and 30 are 3 and 5.
Hence, the HCF of 45 and 30 is 3 × 5 = 15.
HCF (45, 30) = 15
HCF of 45 and 30 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is the HCF of 45 and 30.
No further division can be done.
Hence, HCF (45, 30) = 15
HCF of 45 and 30 by Listing Common Factors
To calculate the HCF of 45 and 30 by listing out the common factors, list the factors as shown below:
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, and they are 1, 3, 5, and 15. Therefore, the highest common factor of 45 and 30 is 15.
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HCF of 45 and 30 Solved Example
Question: 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.
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