HCF of 16 and 144

HCF of 16 and 144 is the largest possible number that divides 16 and 144 exactly without any remainder. The factors of 16 and 144 are 1, 2, 4, 8, 16 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the HCF of 16 and 144 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 16 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 144?

Answer: HCF of 16 and 144 is 16.

Explanation:

The HCF of two non-zero integers, x(16) and y(144), is the highest positive integer m(16) that divides both x(16) and y(144) without any remainder.

Methods to Find HCF of 16 and 144

Let's look at the different methods for finding the HCF of 16 and 144.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

HCF of 16 and 144 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 5 common factors of 16 and 144, that are 1, 2, 4, 8, and 16. Therefore, the highest common factor of 16 and 144 is 16.

HCF of 16 and 144 by Long Division

HCF of 16 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 144 (larger number) by 16 (smaller number).
Step 2: Since the remainder = 0, the divisor (16) is the HCF of 16 and 144.

The corresponding divisor (16) is the HCF of 16 and 144.

HCF of 16 and 144 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 = 144 and Y = 16

HCF(144, 16) = HCF(16, 144 mod 16) = HCF(16, 0)
HCF(16, 0) = 16 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 16 and 144 is 16.

☛ Also Check:

HCF of 16 and 144 Examples

Example 1: Find the HCF of 16 and 144, if their LCM is 144.

Solution:

∵ LCM × HCF = 16 × 144
⇒ HCF(16, 144) = (16 × 144)/144 = 16
Therefore, the highest common factor of 16 and 144 is 16.
Example 2: For two numbers, HCF = 16 and LCM = 144. If one number is 144, find the other number.

Solution:

Given: HCF (x, 144) = 16 and LCM (x, 144) = 144
∵ HCF × LCM = 144 × (x)
⇒ x = (HCF × LCM)/144
⇒ x = (16 × 144)/144
⇒ x = 16
Therefore, the other number is 16.
Example 3: Find the highest number that divides 16 and 144 exactly.

Solution:

The highest number that divides 16 and 144 exactly is their highest common factor, i.e. HCF of 16 and 144.
⇒ Factors of 16 and 144:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the HCF of 16 and 144 is 16.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 16 and 144

What is the HCF of 16 and 144?

The HCF of 16 and 144 is 16. To calculate the Highest common factor of 16 and 144, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the highest factor that exactly divides both 16 and 144, i.e., 16.

How to Find the HCF of 16 and 144 by Long Division Method?

To find the HCF of 16, 144 using long division method, 144 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 16 and 144?

There are three commonly used methods to find the HCF of 16 and 144.

By Listing Common Factors
By Long Division
By Prime Factorization

If the HCF of 144 and 16 is 16, Find its LCM.

HCF(144, 16) × LCM(144, 16) = 144 × 16
Since the HCF of 144 and 16 = 16
⇒ 16 × LCM(144, 16) = 2304
Therefore, LCM = 144
☛ HCF Calculator

How to Find the HCF of 16 and 144 by Prime Factorization?

To find the HCF of 16 and 144, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 144. Hence, HCF(16, 144) = 2 × 2 × 2 × 2 = 16
☛ Prime Numbers

What is the Relation Between LCM and HCF of 16, 144?

The following equation can be used to express the relation between Least Common Multiple and HCF of 16 and 144, i.e. HCF × LCM = 16 × 144.

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum