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

HCF of 108, 288 and 360

HCF of 108, 288 and 360 is the largest possible number that divides 108, 288 and 360 exactly without any remainder. The factors of 108, 288 and 360 are (1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108), (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288) and (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360) respectively. There are 3 commonly used methods to find the HCF of 108, 288 and 360 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 108, 288 and 360
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 108, 288 and 360?

Answer: HCF of 108, 288 and 360 is 36.

Explanation:

The HCF of three non-zero integers, x(108), y(288) and z(360), is the highest positive integer m(36) that divides x(108), y(288) and z(360) without any remainder.

Methods to Find HCF of 108, 288 and 360

The methods to find the HCF of 108, 288 and 360 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 108, 288 and 360 by Long Division

HCF of 108, 288 and 360 can be represented as HCF of (HCF of 108, 288) and 360. HCF(108, 288, 360) can be thus calculated by first finding HCF(108, 288) using long division and thereafter using this result with 360 to perform long division again.

Step 1: Divide 288 (larger number) by 108 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (108) by the remainder (72). Repeat this process until the remainder = 0.
⇒ HCF(108, 288) = 36.
Step 3: Now to find the HCF of 36 and 360, we will perform a long division on 360 and 36.
Step 4: For remainder = 0, divisor = 36 ⇒ HCF(36, 360) = 36

Thus, HCF(108, 288, 360) = HCF(HCF(108, 288), 360) = 36.

HCF of 108, 288 and 360 by Listing Common Factors

Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
Factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

There are 9 common factors of 108, 288 and 360, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 108, 288 and 360 is 36.

HCF of 108, 288 and 360 by Prime Factorization

Prime factorization of 108, 288 and 360 is (2 × 2 × 3 × 3 × 3), (2 × 2 × 2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 3 × 3 × 5) respectively. As visible, 108, 288 and 360 have common prime factors. Hence, the HCF of 108, 288 and 360 is 2 × 2 × 3 × 3 = 36.

☛ Also Check:

HCF of 108, 288 and 360 Examples

Example 1: Verify the relation between the LCM and HCF of 108, 288 and 360.

Solution:

The relation between the LCM and HCF of 108, 288 and 360 is given as, HCF(108, 288, 360) = [(108 × 288 × 360) × LCM(108, 288, 360)]/[LCM(108, 288) × LCM (288, 360) × LCM(108, 360)]
⇒ Prime factorization of 108, 288 and 360:
- 108 = 2 × 2 × 3 × 3 × 3
- 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
- 360 = 2 × 2 × 2 × 3 × 3 × 5
∴ LCM of (108, 288), (288, 360), (108, 360), and (108, 288, 360) is 864, 1440, 1080, and 4320 respectively.
Now, LHS = HCF(108, 288, 360) = 36.
And, RHS = [(108 × 288 × 360) × LCM(108, 288, 360)]/[LCM(108, 288) × LCM (288, 360) × LCM(108, 360)] = [(11197440) × 4320]/[864 × 1440 × 1080]
LHS = RHS = 36.
Hence verified.
Example 2: Find the highest number that divides 108, 288, and 360 completely.

Solution:

The highest number that divides 108, 288, and 360 exactly is their highest common factor.
- Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 288 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
- Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 108, 288, and 360 is 36.
∴ The highest number that divides 108, 288, and 360 is 36.
Example 3: Calculate the HCF of 108, 288, and 360 using LCM of the given numbers.

Solution:

Prime factorization of 108, 288 and 360 is given as,
- 108 = 2 × 2 × 3 × 3 × 3
- 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3
- 360 = 2 × 2 × 2 × 3 × 3 × 5
LCM(108, 288) = 864, LCM(288, 360) = 1440, LCM(360, 108) = 1080, LCM(108, 288, 360) = 4320
⇒ HCF(108, 288, 360) = [(108 × 288 × 360) × LCM(108, 288, 360)]/[LCM(108, 288) × LCM (288, 360) × LCM(360, 108)]
⇒ HCF(108, 288, 360) = (11197440 × 4320)/(864 × 1440 × 1080)
⇒ HCF(108, 288, 360) = 36.
Therefore, the HCF of 108, 288 and 360 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 108, 288 and 360

What is the HCF of 108, 288 and 360?

The HCF of 108, 288 and 360 is 36. To calculate the HCF of 108, 288 and 360, we need to factor each number (factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108; factors of 288 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288; factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360) and choose the highest factor that exactly divides 108, 288 and 360, i.e., 36.

What are the Methods to Find HCF of 108, 288 and 360?

There are three commonly used methods to find the HCF of 108, 288 and 360.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 108, 288 and 360 by Prime Factorization?

To find the HCF of 108, 288 and 360, we will find the prime factorization of given numbers, i.e. 108 = 2 × 2 × 3 × 3 × 3; 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3; 360 = 2 × 2 × 2 × 3 × 3 × 5.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 108, 288 and 360. Hence, HCF(108, 288, 360) = 2 × 2 × 3 × 3 = 36
☛ What are Prime Numbers?

What is the Relation Between LCM and HCF of 108, 288 and 360?

The following equation can be used to express the relation between Least Common Multiple and HCF of 108, 288 and 360, i.e. HCF(108, 288, 360) = [(108 × 288 × 360) × LCM(108, 288, 360)]/[LCM(108, 288) × LCM (288, 360) × LCM(108, 360)].
☛ Highest Common Factor Calculator

Which of the following is HCF of 108, 288 and 360? 36, 375, 405, 367, 395, 397

HCF of 108, 288, 360 will be the number that divides 108, 288, and 360 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