HCF of 3240 and 3600

HCF of 3240 and 3600 is the largest possible number that divides 3240 and 3600 exactly without any remainder. The factors of 3240 and 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600 respectively. There are 3 commonly used methods to find the HCF of 3240 and 3600 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 3240 and 3600
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 3240 and 3600?

Answer: HCF of 3240 and 3600 is 360.

Explanation:

The HCF of two non-zero integers, x(3240) and y(3600), is the highest positive integer m(360) that divides both x(3240) and y(3600) without any remainder.

Methods to Find HCF of 3240 and 3600

Let's look at the different methods for finding the HCF of 3240 and 3600.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 3240 and 3600 by Listing Common Factors

Factors of 3240: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240
Factors of 3600: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600

There are 24 common factors of 3240 and 3600, that are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 180, 60, 72, 90, 360, and 120. Therefore, the highest common factor of 3240 and 3600 is 360.

HCF of 3240 and 3600 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 3600 and Y = 3240

HCF(3600, 3240) = HCF(3240, 3600 mod 3240) = HCF(3240, 360)
HCF(3240, 360) = HCF(360, 3240 mod 360) = HCF(360, 0)
HCF(360, 0) = 360 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 3240 and 3600 is 360.

HCF of 3240 and 3600 by Long Division

HCF of 3240 and 3600 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 3600 (larger number) by 3240 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3240) by the remainder (360).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (360) is the HCF of 3240 and 3600.

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HCF of 3240 and 3600 Examples

Example 1: Find the HCF of 3240 and 3600, if their LCM is 32400.

Solution:

∵ LCM × HCF = 3240 × 3600
⇒ HCF(3240, 3600) = (3240 × 3600)/32400 = 360
Therefore, the highest common factor of 3240 and 3600 is 360.
Example 2: Find the highest number that divides 3240 and 3600 exactly.

Solution:

The highest number that divides 3240 and 3600 exactly is their highest common factor, i.e. HCF of 3240 and 3600.
⇒ Factors of 3240 and 3600:
- Factors of 3240 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240
- Factors of 3600 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600
Therefore, the HCF of 3240 and 3600 is 360.
Example 3: The product of two numbers is 11664000. If their HCF is 360, what is their LCM?

Solution:

Given: HCF = 360 and product of numbers = 11664000
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 11664000/360
Therefore, the LCM is 32400.

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FAQs on HCF of 3240 and 3600

What is the HCF of 3240 and 3600?

The HCF of 3240 and 3600 is 360. To calculate the HCF (Highest Common Factor) of 3240 and 3600, we need to factor each number (factors of 3240 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240; factors of 3600 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600) and choose the highest factor that exactly divides both 3240 and 3600, i.e., 360.

What are the Methods to Find HCF of 3240 and 3600?

There are three commonly used methods to find the HCF of 3240 and 3600.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and HCF of 3240, 3600?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 3240 and 3600, i.e. HCF × LCM = 3240 × 3600.

How to Find the HCF of 3240 and 3600 by Long Division Method?

To find the HCF of 3240, 3600 using long division method, 3600 is divided by 3240. The corresponding divisor (360) when remainder equals 0 is taken as HCF.

If the HCF of 3600 and 3240 is 360, Find its LCM.

HCF(3600, 3240) × LCM(3600, 3240) = 3600 × 3240
Since the HCF of 3600 and 3240 = 360
⇒ 360 × LCM(3600, 3240) = 11664000
Therefore, LCM = 32400
☛ Highest Common Factor Calculator

How to Find the HCF of 3240 and 3600 by Prime Factorization?

To find the HCF of 3240 and 3600, we will find the prime factorization of the given numbers, i.e. 3240 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5; 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5.
⇒ Since 2, 2, 2, 3, 3, 5 are common terms in the prime factorization of 3240 and 3600. Hence, HCF(3240, 3600) = 2 × 2 × 2 × 3 × 3 × 5 = 360
☛ What is a Prime Number?

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