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HCF of 4 and 16

HCF of 4 and 16 is the largest possible number that divides 4 and 16 exactly without any remainder. The factors of 4 and 16 are 1, 2, 4 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the HCF of 4 and 16 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 4 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 4 and 16?

Answer: HCF of 4 and 16 is 4.

Explanation:

The HCF of two non-zero integers, x(4) and y(16), is the highest positive integer m(4) that divides both x(4) and y(16) without any remainder.

Methods to Find HCF of 4 and 16

Let's look at the different methods for finding the HCF of 4 and 16.

Listing Common Factors
Long Division Method
Prime Factorization Method

HCF of 4 and 16 by Listing Common Factors

Factors of 4: 1, 2, 4
Factors of 16: 1, 2, 4, 8, 16

There are 3 common factors of 4 and 16, that are 1, 2, and 4. Therefore, the highest common factor of 4 and 16 is 4.

HCF of 4 and 16 by Long Division

HCF of 4 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the HCF of 4 and 16.

The corresponding divisor (4) is the HCF of 4 and 16.

HCF of 4 and 16 by Prime Factorization

Prime factorization of 4 and 16 is (2 × 2) and (2 × 2 × 2 × 2) respectively. As visible, 4 and 16 have common prime factors. Hence, the HCF of 4 and 16 is 2 × 2 = 4.

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HCF of 4 and 16 Examples

Example 1: For two numbers, HCF = 4 and LCM = 16. If one number is 4, find the other number.

Solution:

Given: HCF (z, 4) = 4 and LCM (z, 4) = 16
∵ HCF × LCM = 4 × (z)
⇒ z = (HCF × LCM)/4
⇒ z = (4 × 16)/4
⇒ z = 16
Therefore, the other number is 16.
Example 2: The product of two numbers is 64. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 64
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 64/4
Therefore, the LCM is 16.
Example 3: Find the HCF of 4 and 16, if their LCM is 16.

Solution:

∵ LCM × HCF = 4 × 16
⇒ HCF(4, 16) = (4 × 16)/16 = 4
Therefore, the highest common factor of 4 and 16 is 4.

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FAQs on HCF of 4 and 16

What is the HCF of 4 and 16?

The HCF of 4 and 16 is 4. To calculate the HCF of 4 and 16, we need to factor each number (factors of 4 = 1, 2, 4; factors of 16 = 1, 2, 4, 8, 16) and choose the highest factor that exactly divides both 4 and 16, i.e., 4.

What is the Relation Between LCM and HCF of 4, 16?

The following equation can be used to express the relation between Least Common Multiple and HCF of 4 and 16, i.e. HCF × LCM = 4 × 16.

What are the Methods to Find HCF of 4 and 16?

There are three commonly used methods to find the HCF of 4 and 16.

By Prime Factorization
By Long Division
By Listing Common Factors

If the HCF of 16 and 4 is 4, Find its LCM.

HCF(16, 4) × LCM(16, 4) = 16 × 4
Since the HCF of 16 and 4 = 4
⇒ 4 × LCM(16, 4) = 64
Therefore, LCM = 16
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How to Find the HCF of 4 and 16 by Long Division Method?

To find the HCF of 4, 16 using long division method, 16 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 4 and 16 by Prime Factorization?

To find the HCF of 4 and 16, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 16 = 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 16. Hence, HCF(4, 16) = 2 × 2 = 4
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