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HCF of 16 and 36

HCF of 16 and 36 is the largest possible number that divides 16 and 36 exactly without any remainder. The factors of 16 and 36 are 1, 2, 4, 8, 16 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the HCF of 16 and 36 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 16 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 36?

Answer: HCF of 16 and 36 is 4.

Explanation:

The HCF of two non-zero integers, x(16) and y(36), is the highest positive integer m(4) that divides both x(16) and y(36) without any remainder.

Methods to Find HCF of 16 and 36

Let's look at the different methods for finding the HCF of 16 and 36.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 16 and 36 by Long Division

HCF of 16 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 16 and 36.

HCF of 16 and 36 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 = 36 and Y = 16

HCF(36, 16) = HCF(16, 36 mod 16) = HCF(16, 4)
HCF(16, 4) = HCF(4, 16 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 16 and 36 is 4.

HCF of 16 and 36 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 3 common factors of 16 and 36, that are 1, 2, and 4. Therefore, the highest common factor of 16 and 36 is 4.

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HCF of 16 and 36 Examples

Example 1: Find the highest number that divides 16 and 36 exactly.

Solution:

The highest number that divides 16 and 36 exactly is their highest common factor, i.e. HCF of 16 and 36.
⇒ Factors of 16 and 36:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the HCF of 16 and 36 is 4.
Example 2: For two numbers, HCF = 4 and LCM = 144. If one number is 36, find the other number.

Solution:

Given: HCF (y, 36) = 4 and LCM (y, 36) = 144
∵ HCF × LCM = 36 × (y)
⇒ y = (HCF × LCM)/36
⇒ y = (4 × 144)/36
⇒ y = 16
Therefore, the other number is 16.
Example 3: The product of two numbers is 576. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 576
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 576/4
Therefore, the LCM is 144.

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FAQs on HCF of 16 and 36

What is the HCF of 16 and 36?

The HCF of 16 and 36 is 4. To calculate the Highest common factor of 16 and 36, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides both 16 and 36, i.e., 4.

What are the Methods to Find HCF of 16 and 36?

There are three commonly used methods to find the HCF of 16 and 36.

By Listing Common Factors
By Long Division
By Prime Factorization

If the HCF of 36 and 16 is 4, Find its LCM.

HCF(36, 16) × LCM(36, 16) = 36 × 16
Since the HCF of 36 and 16 = 4
⇒ 4 × LCM(36, 16) = 576
Therefore, LCM = 144
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How to Find the HCF of 16 and 36 by Long Division Method?

To find the HCF of 16, 36 using long division method, 36 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 16 and 36 by Prime Factorization?

To find the HCF of 16 and 36, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 36. Hence, HCF(16, 36) = 2 × 2 = 4
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What is the Relation Between LCM and HCF of 16, 36?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 16 and 36, i.e. HCF × LCM = 16 × 36.

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