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HCF of 4 and 10

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

1.	HCF of 4 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 4 and 10?

Answer: HCF of 4 and 10 is 2.

Explanation:

The HCF of two non-zero integers, x(4) and y(10), is the highest positive integer m(2) that divides both x(4) and y(10) without any remainder.

Methods to Find HCF of 4 and 10

Let's look at the different methods for finding the HCF of 4 and 10.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 4 and 10 by Long Division

HCF of 4 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10 (larger number) by 4 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 4 and 10.

HCF of 4 and 10 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 = 10 and Y = 4

HCF(10, 4) = HCF(4, 10 mod 4) = HCF(4, 2)
HCF(4, 2) = HCF(2, 4 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 4 and 10 is 2.

HCF of 4 and 10 by Listing Common Factors

Factors of 4: 1, 2, 4
Factors of 10: 1, 2, 5, 10

There are 2 common factors of 4 and 10, that are 1 and 2. Therefore, the highest common factor of 4 and 10 is 2.

☛ Also Check:

HCF of 4 and 10 Examples

Example 1: Find the HCF of 4 and 10, if their LCM is 20.

Solution:

∵ LCM × HCF = 4 × 10
⇒ HCF(4, 10) = (4 × 10)/20 = 2
Therefore, the highest common factor of 4 and 10 is 2.
Example 2: Find the highest number that divides 4 and 10 exactly.

Solution:

The highest number that divides 4 and 10 exactly is their highest common factor, i.e. HCF of 4 and 10.
⇒ Factors of 4 and 10:
- Factors of 4 = 1, 2, 4
- Factors of 10 = 1, 2, 5, 10
Therefore, the HCF of 4 and 10 is 2.
Example 3: For two numbers, HCF = 2 and LCM = 20. If one number is 10, find the other number.

Solution:

Given: HCF (x, 10) = 2 and LCM (x, 10) = 20
∵ HCF × LCM = 10 × (x)
⇒ x = (HCF × LCM)/10
⇒ x = (2 × 20)/10
⇒ x = 4
Therefore, the other number is 4.

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FAQs on HCF of 4 and 10

What is the HCF of 4 and 10?

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

What is the Relation Between LCM and HCF of 4, 10?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 4 and 10, i.e. HCF × LCM = 4 × 10.

How to Find the HCF of 4 and 10 by Prime Factorization?

To find the HCF of 4 and 10, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 4 and 10. Hence, HCF (4, 10) = 2.
☛ What is a Prime Number?

If the HCF of 10 and 4 is 2, Find its LCM.

HCF(10, 4) × LCM(10, 4) = 10 × 4
Since the HCF of 10 and 4 = 2
⇒ 2 × LCM(10, 4) = 40
Therefore, LCM = 20
☛ Highest Common Factor Calculator

How to Find the HCF of 4 and 10 by Long Division Method?

To find the HCF of 4, 10 using long division method, 10 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 4 and 10?

There are three commonly used methods to find the HCF of 4 and 10.

By Prime Factorization
By Listing Common Factors
By Long Division

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