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HCF of 20 and 35

HCF of 20 and 35 is the largest possible number that divides 20 and 35 exactly without any remainder. The factors of 20 and 35 are 1, 2, 4, 5, 10, 20 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the HCF of 20 and 35 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 20 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 20 and 35?

Answer: HCF of 20 and 35 is 5.

Explanation:

The HCF of two non-zero integers, x(20) and y(35), is the highest positive integer m(5) that divides both x(20) and y(35) without any remainder.

Methods to Find HCF of 20 and 35

Let's look at the different methods for finding the HCF of 20 and 35.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

HCF of 20 and 35 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 = 35 and Y = 20

HCF(35, 20) = HCF(20, 35 mod 20) = HCF(20, 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 20 and 35 is 5.

HCF of 20 and 35 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 35: 1, 5, 7, 35

There are 2 common factors of 20 and 35, that are 1 and 5. Therefore, the highest common factor of 20 and 35 is 5.

HCF of 20 and 35 by Long Division

HCF of 20 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 20 and 35.

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HCF of 20 and 35 Examples

Example 1: For two numbers, HCF = 5 and LCM = 140. If one number is 35, find the other number.

Solution:

Given: HCF (y, 35) = 5 and LCM (y, 35) = 140
∵ HCF × LCM = 35 × (y)
⇒ y = (HCF × LCM)/35
⇒ y = (5 × 140)/35
⇒ y = 20
Therefore, the other number is 20.
Example 2: Find the HCF of 20 and 35, if their LCM is 140.

Solution:

∵ LCM × HCF = 20 × 35
⇒ HCF(20, 35) = (20 × 35)/140 = 5
Therefore, the highest common factor of 20 and 35 is 5.
Example 3: Find the highest number that divides 20 and 35 exactly.

Solution:

The highest number that divides 20 and 35 exactly is their highest common factor, i.e. HCF of 20 and 35.
⇒ Factors of 20 and 35:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 35 = 1, 5, 7, 35
Therefore, the HCF of 20 and 35 is 5.

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FAQs on HCF of 20 and 35

What is the HCF of 20 and 35?

The HCF of 20 and 35 is 5. To calculate the HCF (Highest Common Factor) of 20 and 35, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 35 = 1, 5, 7, 35) and choose the highest factor that exactly divides both 20 and 35, i.e., 5.

If the HCF of 35 and 20 is 5, Find its LCM.

HCF(35, 20) × LCM(35, 20) = 35 × 20
Since the HCF of 35 and 20 = 5
⇒ 5 × LCM(35, 20) = 700
Therefore, LCM = 140
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What are the Methods to Find HCF of 20 and 35?

There are three commonly used methods to find the HCF of 20 and 35.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and HCF of 20, 35?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 20 and 35, i.e. HCF × LCM = 20 × 35.

How to Find the HCF of 20 and 35 by Long Division Method?

To find the HCF of 20, 35 using long division method, 35 is divided by 20. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

How to Find the HCF of 20 and 35 by Prime Factorization?

To find the HCF of 20 and 35, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 35 = 5 × 7.
⇒ Since 5 is the only common prime factor of 20 and 35. Hence, HCF (20, 35) = 5.
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