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HCF of 396 and 1080

HCF of 396 and 1080 is the largest possible number that divides 396 and 1080 exactly without any remainder. The factors of 396 and 1080 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080 respectively. There are 3 commonly used methods to find the HCF of 396 and 1080 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 396 and 1080
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 396 and 1080?

Answer: HCF of 396 and 1080 is 36.

Explanation:

The HCF of two non-zero integers, x(396) and y(1080), is the highest positive integer m(36) that divides both x(396) and y(1080) without any remainder.

Methods to Find HCF of 396 and 1080

Let's look at the different methods for finding the HCF of 396 and 1080.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 396 and 1080 by Long Division

HCF of 396 and 1080 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1080 (larger number) by 396 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (396) by the remainder (288).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (36) is the HCF of 396 and 1080.

HCF of 396 and 1080 by Prime Factorization

Prime factorization of 396 and 1080 is (2 × 2 × 3 × 3 × 11) and (2 × 2 × 2 × 3 × 3 × 3 × 5) respectively. As visible, 396 and 1080 have common prime factors. Hence, the HCF of 396 and 1080 is 2 × 2 × 3 × 3 = 36.

HCF of 396 and 1080 by Listing Common Factors

Factors of 396: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
Factors of 1080: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080

There are 9 common factors of 396 and 1080, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 396 and 1080 is 36.

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HCF of 396 and 1080 Examples

Example 1: The product of two numbers is 427680. If their HCF is 36, what is their LCM?

Solution:

Given: HCF = 36 and product of numbers = 427680
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 427680/36
Therefore, the LCM is 11880.
Example 2: Find the highest number that divides 396 and 1080 exactly.

Solution:

The highest number that divides 396 and 1080 exactly is their highest common factor, i.e. HCF of 396 and 1080.
⇒ Factors of 396 and 1080:
- Factors of 396 = 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
- Factors of 1080 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080
Therefore, the HCF of 396 and 1080 is 36.
Example 3: For two numbers, HCF = 36 and LCM = 11880. If one number is 396, find the other number.

Solution:

Given: HCF (x, 396) = 36 and LCM (x, 396) = 11880
∵ HCF × LCM = 396 × (x)
⇒ x = (HCF × LCM)/396
⇒ x = (36 × 11880)/396
⇒ x = 1080
Therefore, the other number is 1080.

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FAQs on HCF of 396 and 1080

What is the HCF of 396 and 1080?

The HCF of 396 and 1080 is 36. To calculate the Highest common factor (HCF) of 396 and 1080, we need to factor each number (factors of 396 = 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396; factors of 1080 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080) and choose the highest factor that exactly divides both 396 and 1080, i.e., 36.

If the HCF of 1080 and 396 is 36, Find its LCM.

HCF(1080, 396) × LCM(1080, 396) = 1080 × 396
Since the HCF of 1080 and 396 = 36
⇒ 36 × LCM(1080, 396) = 427680
Therefore, LCM = 11880
☛ Highest Common Factor Calculator

How to Find the HCF of 396 and 1080 by Long Division Method?

To find the HCF of 396, 1080 using long division method, 1080 is divided by 396. The corresponding divisor (36) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 396 and 1080?

There are three commonly used methods to find the HCF of 396 and 1080.

By Long Division
By Euclidean Algorithm
By Prime Factorization

What is the Relation Between LCM and HCF of 396, 1080?

The following equation can be used to express the relation between Least Common Multiple and HCF of 396 and 1080, i.e. HCF × LCM = 396 × 1080.

How to Find the HCF of 396 and 1080 by Prime Factorization?

To find the HCF of 396 and 1080, we will find the prime factorization of the given numbers, i.e. 396 = 2 × 2 × 3 × 3 × 11; 1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 396 and 1080. Hence, HCF(396, 1080) = 2 × 2 × 3 × 3 = 36
☛ What is a Prime Number?

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