A day full of math games & activities. Find one near you.

HCF of 72, 108 and 180

HCF of 72, 108 and 180 is the largest possible number that divides 72, 108 and 180 exactly without any remainder. The factors of 72, 108 and 180 are (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), (1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108) and (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) respectively. There are 3 commonly used methods to find the HCF of 72, 108 and 180 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 72, 108 and 180
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 72, 108 and 180?

Answer: HCF of 72, 108 and 180 is 36.

Explanation:

The HCF of three non-zero integers, x(72), y(108) and z(180), is the highest positive integer m(36) that divides x(72), y(108) and z(180) without any remainder.

Methods to Find HCF of 72, 108 and 180

Let's look at the different methods for finding the HCF of 72, 108 and 180.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 72, 108 and 180 by Long Division

HCF of 72, 108 and 180 can be represented as HCF of (HCF of 72, 108) and 180. HCF(72, 108, 180) can be thus calculated by first finding HCF(72, 108) using long division and thereafter using this result with 180 to perform long division again.

Step 1: Divide 108 (larger number) by 72 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (36). Repeat this process until the remainder = 0.
⇒ HCF(72, 108) = 36.
Step 3: Now to find the HCF of 36 and 180, we will perform a long division on 180 and 36.
Step 4: For remainder = 0, divisor = 36 ⇒ HCF(36, 180) = 36

Thus, HCF(72, 108, 180) = HCF(HCF(72, 108), 180) = 36.

HCF of 72, 108 and 180 by Listing Common Factors

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

There are 9 common factors of 72, 108 and 180, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 72, 108 and 180 is 36.

HCF of 72, 108 and 180 by Prime Factorization

Prime factorization of 72, 108 and 180 is (2 × 2 × 2 × 3 × 3), (2 × 2 × 3 × 3 × 3) and (2 × 2 × 3 × 3 × 5) respectively. As visible, 72, 108 and 180 have common prime factors. Hence, the HCF of 72, 108 and 180 is 2 × 2 × 3 × 3 = 36.

☛ Also Check:

HCF of 72, 108 and 180 Examples

Example 1: Verify the relation between the LCM and HCF of 72, 108 and 180.

Solution:

The relation between the LCM and HCF of 72, 108 and 180 is given as, HCF(72, 108, 180) = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(72, 180)]
⇒ Prime factorization of 72, 108 and 180:
- 72 = 2 × 2 × 2 × 3 × 3
- 108 = 2 × 2 × 3 × 3 × 3
- 180 = 2 × 2 × 3 × 3 × 5
∴ LCM of (72, 108), (108, 180), (72, 180), and (72, 108, 180) is 216, 540, 360, and 1080 respectively.
Now, LHS = HCF(72, 108, 180) = 36.
And, RHS = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(72, 180)] = [(1399680) × 1080]/[216 × 540 × 360]
LHS = RHS = 36.
Hence verified.
Example 2: Calculate the HCF of 72, 108, and 180 using LCM of the given numbers.

Solution:

Prime factorization of 72, 108 and 180 is given as,
- 72 = 2 × 2 × 2 × 3 × 3
- 108 = 2 × 2 × 3 × 3 × 3
- 180 = 2 × 2 × 3 × 3 × 5
LCM(72, 108) = 216, LCM(108, 180) = 540, LCM(180, 72) = 360, LCM(72, 108, 180) = 1080
⇒ HCF(72, 108, 180) = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(180, 72)]
⇒ HCF(72, 108, 180) = (1399680 × 1080)/(216 × 540 × 360)
⇒ HCF(72, 108, 180) = 36.
Therefore, the HCF of 72, 108 and 180 is 36.
Example 3: Find the highest number that divides 72, 108, and 180 completely.

Solution:

The highest number that divides 72, 108, and 180 exactly is their highest common factor.
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 72, 108, and 180 is 36.
∴ The highest number that divides 72, 108, and 180 is 36.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 72, 108 and 180

What is the HCF of 72, 108 and 180?

The HCF of 72, 108 and 180 is 36. To calculate the highest common factor of 72, 108 and 180, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108; factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) and choose the highest factor that exactly divides 72, 108 and 180, i.e., 36.

How to Find the HCF of 72, 108 and 180 by Prime Factorization?

To find the HCF of 72, 108 and 180, we will find the prime factorization of given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 108 = 2 × 2 × 3 × 3 × 3; 180 = 2 × 2 × 3 × 3 × 5.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 72, 108 and 180. Hence, HCF(72, 108, 180) = 2 × 2 × 3 × 3 = 36
☛ Prime Number

What are the Methods to Find HCF of 72, 108 and 180?

There are three commonly used methods to find the HCF of 72, 108 and 180.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 72, 108 and 180?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 72, 108 and 180, i.e. HCF(72, 108, 180) = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(72, 180)].
☛ HCF Calculator

Which of the following is HCF of 72, 108 and 180? 36, 217, 190, 222, 198, 186, 222, 198, 188

HCF of 72, 108, 180 will be the number that divides 72, 108, and 180 without leaving any remainder. The only number that satisfies the given condition is 36.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum