The HCF of 120, 144 and 204 is 12. The greatest number that divides 120, 144, and 204 exactly without leaving any remainder is the HCF of these numbers. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 120, 144 and 204. The factors of 120, 144, and 204 are:
120 → 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
144 → 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
204 → 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204)
Also read: Highest common factor
What is the HCF of 120, 144 and 204?
The answer to this question is 12. This article shows how to find the HCF of 120, 144 and 204 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 120, 144 and 204?
There are three methods to find the HCF of 120, 144 and 204:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 120, 144 and 204 by Prime Factorisation Method
The prime factorisation of 120, 144 and 204 is given by:
Prime factorisation of 120 = (2 × 2 × 2 × 3 × 5)
Prime factorisation of 144 = (2 × 2 × 2 × 2 × 3 × 3)
Prime factorisation of 204 = (2 × 2 × 3 × 17)
The common prime factors are 2, 2 and 3.
Hence, the HCF of 120, 144 and 204 is 2 × 2 × 3 = 12.
HCF (120, 144, 204) = 12
HCF of 120, 144 and 204 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 120, 144 and 204.
No further division can be done.
Hence, HCF (120, 144, 204) = 12
HCF of 120, 144 and 204 by Listing Common Factors
To calculate the HCF of 120, 144 and 204 by listing out the common factors, list the factors as shown below:
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 204 = 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
Therefore, the HCF of 120, 144, and 204 is 12.
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Solved Example
Find the highest number that divides 120, 144, and 204 completely.
Solution:
The highest number that divides 120, 144, and 204 exactly is their highest common factor.
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 204 = 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The HCF of 120, 144, and 204 is 12.
Therefore, the highest number that divides 120, 144, and 204 is 12.
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