The HCF of 45 and 180 is 45. The highest number that divides 45 and 180 perfectly and without leaving any leftover is the HCF of these numbers. The factors of 45 and 180 are, respectively, (1, 3, 5, 9, 15, 45) and (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 30, 36, 45, 60, 90, 180). The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 45 and 180.
Also read: Highest common factor
What is the HCF of 45 and 180?
The answer to this question is 45. This article shows the HCF of 45 and 180 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 180?
There are three methods to find the HCF of 45 and 180:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 45 and 180 by Prime Factorisation Method
The prime factorisation of 45 and 180 is given by:
Prime factorisation of 45 = (3 × 3 × 5)
Prime factorisation of 180 = (2 × 2 × 3 × 3 × 5)
Hence, the HCF of 45 and 180 is 3 × 3 × 5 = 45.
HCF (45, 180) = 45
HCF of 45 and 180 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 45 and 180.
No further division can be done.
Hence, HCF (45, 180) = 45
HCF of 45 and 180 by Listing the Factors
To calculate the HCF of 45 and 180 by listing out the common factors, list the factors as shown below:
Factors of 45 = 1, 3, 5, 9, 15, 45
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Therefore, the HCF of 45 and 180 is 45.
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Video Lesson on Properties of HCF and LCM
HCF of 45 and 180 Solved Example
Find the highest number that divides 45 and 180 exactly.
Solution:
The highest number that divides 45 and 180 exactly is their highest common factor, i.e. HCF of 45 and 180.
⇒ Factors of 45 and 180:
Factors of 45 = 1, 3, 5, 9, 15, 45
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Therefore, the HCF of 45 and 180 is 45.
Frequently Asked Questions on HCF of 45 and 180
What is the HCF of 45 and 180?
How to Find the HCF of 45 and 180 by Prime Factorisation?
⇒ Since 3, 3, 5 are common terms in the prime factorization of 45 and 180. Hence, HCF(45, 180) = 3 × 3 × 5 = 45
What are the Methods to Find HCF of 45 and 180?
By Long Division
By Listing Common Factors
By Prime Factorisation
If the HCF of 180 and 45 is 45, Find its LCM.
Since the HCF of 180 and 45 = 45
⇒ 45 × LCM(180, 45) = 8100
Therefore, LCM = 180
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