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HCF of 405 and 2520

HCF of 405 and 2520 is the largest possible number that divides 405 and 2520 exactly without any remainder. The factors of 405 and 2520 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520 respectively. There are 3 commonly used methods to find the HCF of 405 and 2520 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 405 and 2520
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 405 and 2520?

Answer: HCF of 405 and 2520 is 45.

Explanation:

The HCF of two non-zero integers, x(405) and y(2520), is the highest positive integer m(45) that divides both x(405) and y(2520) without any remainder.

Methods to Find HCF of 405 and 2520

Let's look at the different methods for finding the HCF of 405 and 2520.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

HCF of 405 and 2520 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 = 2520 and Y = 405

HCF(2520, 405) = HCF(405, 2520 mod 405) = HCF(405, 90)
HCF(405, 90) = HCF(90, 405 mod 90) = HCF(90, 45)
HCF(90, 45) = HCF(45, 90 mod 45) = HCF(45, 0)
HCF(45, 0) = 45 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 405 and 2520 is 45.

HCF of 405 and 2520 by Prime Factorization

Prime factorization of 405 and 2520 is (3 × 3 × 3 × 3 × 5) and (2 × 2 × 2 × 3 × 3 × 5 × 7) respectively. As visible, 405 and 2520 have common prime factors. Hence, the HCF of 405 and 2520 is 3 × 3 × 5 = 45.

HCF of 405 and 2520 by Listing Common Factors

Factors of 405: 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
Factors of 2520: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520

There are 6 common factors of 405 and 2520, that are 1, 3, 5, 9, 45, and 15. Therefore, the highest common factor of 405 and 2520 is 45.

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HCF of 405 and 2520 Examples

Example 1: Find the HCF of 405 and 2520, if their LCM is 22680.

Solution:

∵ LCM × HCF = 405 × 2520
⇒ HCF(405, 2520) = (405 × 2520)/22680 = 45
Therefore, the highest common factor of 405 and 2520 is 45.
Example 2: Find the highest number that divides 405 and 2520 exactly.

Solution:

The highest number that divides 405 and 2520 exactly is their highest common factor, i.e. HCF of 405 and 2520.
⇒ Factors of 405 and 2520:
- Factors of 405 = 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
- Factors of 2520 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520
Therefore, the HCF of 405 and 2520 is 45.
Example 3: The product of two numbers is 1020600. If their HCF is 45, what is their LCM?

Solution:

Given: HCF = 45 and product of numbers = 1020600
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1020600/45
Therefore, the LCM is 22680.

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FAQs on HCF of 405 and 2520

What is the HCF of 405 and 2520?

The HCF of 405 and 2520 is 45. To calculate the HCF (Highest Common Factor) of 405 and 2520, we need to factor each number (factors of 405 = 1, 3, 5, 9, 15, 27, 45, 81, 135, 405; factors of 2520 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520) and choose the highest factor that exactly divides both 405 and 2520, i.e., 45.

How to Find the HCF of 405 and 2520 by Long Division Method?

To find the HCF of 405, 2520 using long division method, 2520 is divided by 405. The corresponding divisor (45) when remainder equals 0 is taken as HCF.

How to Find the HCF of 405 and 2520 by Prime Factorization?

To find the HCF of 405 and 2520, we will find the prime factorization of the given numbers, i.e. 405 = 3 × 3 × 3 × 3 × 5; 2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 405 and 2520. Hence, HCF(405, 2520) = 3 × 3 × 5 = 45
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What is the Relation Between LCM and HCF of 405, 2520?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 405 and 2520, i.e. HCF × LCM = 405 × 2520.

If the HCF of 2520 and 405 is 45, Find its LCM.

HCF(2520, 405) × LCM(2520, 405) = 2520 × 405
Since the HCF of 2520 and 405 = 45
⇒ 45 × LCM(2520, 405) = 1020600
Therefore, LCM = 22680
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What are the Methods to Find HCF of 405 and 2520?

There are three commonly used methods to find the HCF of 405 and 2520.

By Long Division
By Prime Factorization
By Listing Common Factors

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