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HCF of 15 and 20

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

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

What is HCF of 15 and 20?

Answer: HCF of 15 and 20 is 5.

Explanation:

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

Methods to Find HCF of 15 and 20

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

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 15 and 20 by Prime Factorization

Prime factorization of 15 and 20 is (3 × 5) and (2 × 2 × 5) respectively. As visible, 15 and 20 have only one common prime factor i.e. 5. Hence, the HCF of 15 and 20 is 5.

HCF of 15 and 20 by Long Division

HCF of 15 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 15 and 20.

HCF of 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.

Here X = 20 and Y = 15

HCF(20, 15) = HCF(15, 20 mod 15) = HCF(15, 5)
HCF(15, 5) = HCF(5, 15 mod 5) = HCF(5, 0)
HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

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

☛ Also Check:

HCF of 15 and 20 Examples

Example 1: Find the HCF of 15 and 20, if their LCM is 60.

Solution:

∵ LCM × HCF = 15 × 20
⇒ HCF(15, 20) = (15 × 20)/60 = 5
Therefore, the highest common factor of 15 and 20 is 5.
Example 2: For two numbers, HCF = 5 and LCM = 60. If one number is 15, find the other number.

Solution:

Given: HCF (x, 15) = 5 and LCM (x, 15) = 60
∵ HCF × LCM = 15 × (x)
⇒ x = (HCF × LCM)/15
⇒ x = (5 × 60)/15
⇒ x = 20
Therefore, the other number is 20.
Example 3: Find the highest number that divides 15 and 20 exactly.

Solution:

The highest number that divides 15 and 20 exactly is their highest common factor, i.e. HCF of 15 and 20.
⇒ Factors of 15 and 20:
- Factors of 15 = 1, 3, 5, 15
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the HCF of 15 and 20 is 5.

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FAQs on HCF of 15 and 20

What is the HCF of 15 and 20?

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

What is the Relation Between LCM and HCF of 15, 20?

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

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

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

How to Find the HCF of 15 and 20 by Long Division Method?

To find the HCF of 15, 20 using long division method, 20 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

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

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

By Long Division
By Prime Factorization
By Listing Common Factors

If the HCF of 20 and 15 is 5, Find its LCM.

HCF(20, 15) × LCM(20, 15) = 20 × 15
Since the HCF of 20 and 15 = 5
⇒ 5 × LCM(20, 15) = 300
Therefore, LCM = 60
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