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HCF of 5, 15 and 20

HCF of 5, 15 and 20 is the largest possible number that divides 5, 15 and 20 exactly without any remainder. The factors of 5, 15 and 20 are (1, 5), (1, 3, 5, 15) and (1, 2, 4, 5, 10, 20) respectively. There are 3 commonly used methods to find the HCF of 5, 15 and 20 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 5, 15 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 5, 15 and 20?

Answer: HCF of 5, 15 and 20 is 5.

Explanation:

The HCF of three non-zero integers, x(5), y(15) and z(20), is the highest positive integer m(5) that divides x(5), y(15) and z(20) without any remainder.

Methods to Find HCF of 5, 15 and 20

The methods to find the HCF of 5, 15 and 20 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 5, 15 and 20 by Listing Common Factors

Factors of 5: 1, 5
Factors of 15: 1, 3, 5, 15
Factors of 20: 1, 2, 4, 5, 10, 20

There are 2 common factors of 5, 15 and 20, that are 1 and 5. Therefore, the highest common factor of 5, 15 and 20 is 5.

HCF of 5, 15 and 20 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.

HCF(5, 15, 20) = HCF(HCF(5, 15), 20)

HCF(15, 5) = HCF(5, 15 mod 5) = HCF(5, 0)
HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(5, 20)

HCF(20, 5) = HCF(5, 20 mod 5) = HCF(5, 0)
HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 5, 15 and 20 is 5.

HCF of 5, 15 and 20 by Long Division

HCF of 5, 15 and 20 can be represented as HCF of (HCF of 5, 15) and 20. HCF(5, 15, 20) can be thus calculated by first finding HCF(5, 15) using long division and thereafter using this result with 20 to perform long division again.

Step 1: Divide 15 (larger number) by 5 (smaller number).
Step 2: Since the remainder = 0, the divisor (5) is the HCF(5, 15) = 5.
Step 3: Now to find the HCF of 5 and 20, we will perform a long division on 20 and 5.
Step 4: For remainder = 0, divisor = 5 ⇒ HCF(5, 20) = 5

Thus, HCF(5, 15, 20) = HCF(HCF(5, 15), 20) = 5.

☛ Also Check:

HCF of 5, 15 and 20 Examples

Example 1: Verify the relation between the LCM and HCF of 5, 15 and 20.

Solution:

The relation between the LCM and HCF of 5, 15 and 20 is given as, HCF(5, 15, 20) = [(5 × 15 × 20) × LCM(5, 15, 20)]/[LCM(5, 15) × LCM (15, 20) × LCM(5, 20)]
⇒ Prime factorization of 5, 15 and 20:
- 5 = 5
- 15 = 3 × 5
- 20 = 2 × 2 × 5
∴ LCM of (5, 15), (15, 20), (5, 20), and (5, 15, 20) is 15, 60, 20, and 60 respectively.
Now, LHS = HCF(5, 15, 20) = 5.
And, RHS = [(5 × 15 × 20) × LCM(5, 15, 20)]/[LCM(5, 15) × LCM (15, 20) × LCM(5, 20)] = [(1500) × 60]/[15 × 60 × 20]
LHS = RHS = 5.
Hence verified.
Example 2: Find the highest number that divides 5, 15, and 20 completely.

Solution:

The highest number that divides 5, 15, and 20 exactly is their highest common factor.
- Factors of 5 = 1, 5
- Factors of 15 = 1, 3, 5, 15
- Factors of 20 = 1, 2, 4, 5, 10, 20
The HCF of 5, 15, and 20 is 5.
∴ The highest number that divides 5, 15, and 20 is 5.
Example 3: Calculate the HCF of 5, 15, and 20 using LCM of the given numbers.

Solution:

Prime factorization of 5, 15 and 20 is given as,
- 5 = 5
- 15 = 3 × 5
- 20 = 2 × 2 × 5
LCM(5, 15) = 15, LCM(15, 20) = 60, LCM(20, 5) = 20, LCM(5, 15, 20) = 60
⇒ HCF(5, 15, 20) = [(5 × 15 × 20) × LCM(5, 15, 20)]/[LCM(5, 15) × LCM (15, 20) × LCM(20, 5)]
⇒ HCF(5, 15, 20) = (1500 × 60)/(15 × 60 × 20)
⇒ HCF(5, 15, 20) = 5.
Therefore, the HCF of 5, 15 and 20 is 5.

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FAQs on HCF of 5, 15 and 20

What is the HCF of 5, 15 and 20?

The HCF of 5, 15 and 20 is 5. To calculate the highest common factor of 5, 15 and 20, we need to factor each number (factors of 5 = 1, 5; factors of 15 = 1, 3, 5, 15; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides 5, 15 and 20, i.e., 5.

Which of the following is HCF of 5, 15 and 20? 5, 67, 42, 34, 31, 58, 41, 65, 26

HCF of 5, 15, 20 will be the number that divides 5, 15, and 20 without leaving any remainder. The only number that satisfies the given condition is 5.

What are the Methods to Find HCF of 5, 15 and 20?

There are three commonly used methods to find the HCF of 5, 15 and 20.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 5, 15 and 20 by Prime Factorization?

To find the HCF of 5, 15 and 20, we will find the prime factorization of given numbers, i.e. 5 = 5; 15 = 3 × 5; 20 = 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 5, 15 and 20. Hence, HCF(5, 15, 20) = 5.
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What is the Relation Between LCM and HCF of 5, 15 and 20?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 5, 15 and 20, i.e. HCF(5, 15, 20) = [(5 × 15 × 20) × LCM(5, 15, 20)]/[LCM(5, 15) × LCM (15, 20) × LCM(5, 20)].
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