The HCF of 135 and 225 is 45. The greatest possible number that divides 135 and 225 perfectly without any remainder is the HCF of 135 and 225. 1, 3, 5, 9, 15, 27, 45, 135 and 1, 3, 5, 9, 15, 25, 45, 75, 225 are the factors of 135 and 225, respectively. The long division, listing common factors and prime factorisation are the three most prevalent methods for calculating the HCF of 135 and 225.
Also read: Highest common factor
What is the HCF of 135 and 225?
The answer to this question is 45. This article shows the HCF of 135 and 225 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 135 and 225?
There are three methods to find the HCF of 135 and 225:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 135 and 225 by Prime Factorisation Method
The prime factorisation of 135 and 225 is given by:
Prime factorisation of 135 = (3 × 3 × 3 × 5)
Prime factorisation of 225 = (3 × 3 × 5 × 5)
Hence the common prime factors of 135 and 225 are 3, 3 and 5, and the HCF of 135 and 225 is 3 × 3 × 5 = 45.
HCF (135, 225) = 45
HCF of 135 and 225 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 135 and 225.
No further division can be done.
Hence, HCF (135, 225) = 45
HCF of 135 and 225 by Listing the Factors
To calculate the HCF of 135 and 225 by listing out the common factors, list the factors as shown below:
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225
There are 6 common factors of 135 and 225, and they are 1, 3, 5, 9, 15, and 45. Therefore, the highest common factor of 135 and 225 is 45.
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HCF of 135 and 225 Solved Example
Find the highest number that divides 135 and 225 exactly.
Solution:
The highest number that divides 135 and 225 exactly is their highest common factor, i.e. HCF of 135 and 225.
⇒ Factors of 135 and 225:
Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
Factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
Therefore, the HCF of 135 and 225 is 45.
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