HCF of 120 144 and 204

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.

HCF of 120 144 and 204 1 HCF of 120 144 and 204 2

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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Video Lesson on Properties of HCF and LCM

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.

Frequently Asked Questions on HCF of 120, 144 and 204

Q1

What is the HCF of 120, 144 and 204?

The HCF of 120, 144 and 204 is 12. To calculate the highest common factor of 120, 144 and 204, we need to factor each number and choose the highest factor that exactly divides 120, 144 and 204, i.e. 12.
Q2

How to find the HCF of 120, 144 and 204 by prime factorisation?

To find the HCF of 120, 144 and 204, we will find the prime factorisation of given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 144 = 2 × 2 × 2 × 2 × 3 × 3; 204 = 2 × 2 × 3 × 17. ⇒ Since 2, 2 and 3 are common factors in the prime factorisation of 120, 144 and 204, HCF(120, 144, 204) = 2 × 2 × 3 = 12
Q3

What are the methods to find HCF of 120, 144 and 204?

There are three commonly used methods to find the HCF of 120, 144 and 204, and they are: Long Division Listing Common Factors Prime Factorisation
Q4

Which of the following is the HCF of 120, 144 and 204? 12, 216, 244, 220, 215, 204

The HCF of 120, 144, 204 will be the number that divides 120, 144, and 204 without leaving any remainder. The only number that satisfies the given condition is 12.
Q5

What is the relation between LCM and HCF of 120, 144 and 204?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 120, 144 and 204, i.e. HCF(120, 144, 204) = [(120 × 144 × 204) × LCM (120, 144, 204)]/[LCM (120, 144) × LCM (144, 204) × LCM (120, 204)].

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