A day full of math games & activities. Find one near you.

HCF of 18 and 48

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

1.	HCF of 18 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 48?

Answer: HCF of 18 and 48 is 6.

Explanation:

The HCF of two non-zero integers, x(18) and y(48), is the highest positive integer m(6) that divides both x(18) and y(48) without any remainder.

Methods to Find HCF of 18 and 48

Let's look at the different methods for finding the HCF of 18 and 48.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

HCF of 18 and 48 by Prime Factorization

Prime factorization of 18 and 48 is (2 × 3 × 3) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 18 and 48 have common prime factors. Hence, the HCF of 18 and 48 is 2 × 3 = 6.

HCF of 18 and 48 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 = 48 and Y = 18

HCF(48, 18) = HCF(18, 48 mod 18) = HCF(18, 12)
HCF(18, 12) = HCF(12, 18 mod 12) = HCF(12, 6)
HCF(12, 6) = HCF(6, 12 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 18 and 48 is 6.

HCF of 18 and 48 by Long Division

HCF of 18 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 18 and 48.

☛ Also Check:

HCF of 18 and 48 Examples

Example 1: The product of two numbers is 864. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 864
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 864/6
Therefore, the LCM is 144.
Example 2: Find the HCF of 18 and 48, if their LCM is 144.

Solution:

∵ LCM × HCF = 18 × 48
⇒ HCF(18, 48) = (18 × 48)/144 = 6
Therefore, the highest common factor of 18 and 48 is 6.
Example 3: For two numbers, HCF = 6 and LCM = 144. If one number is 18, find the other number.

Solution:

Given: HCF (y, 18) = 6 and LCM (y, 18) = 144
∵ HCF × LCM = 18 × (y)
⇒ y = (HCF × LCM)/18
⇒ y = (6 × 144)/18
⇒ y = 48
Therefore, the other number is 48.

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 18 and 48

What is the HCF of 18 and 48?

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

What is the Relation Between LCM and HCF of 18, 48?

The following equation can be used to express the relation between Least Common Multiple and HCF of 18 and 48, i.e. HCF × LCM = 18 × 48.

How to Find the HCF of 18 and 48 by Long Division Method?

To find the HCF of 18, 48 using long division method, 48 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

How to Find the HCF of 18 and 48 by Prime Factorization?

To find the HCF of 18 and 48, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 48. Hence, HCF(18, 48) = 2 × 3 = 6
☛ What is a Prime Number?

What are the Methods to Find HCF of 18 and 48?

There are three commonly used methods to find the HCF of 18 and 48.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the HCF of 48 and 18 is 6, Find its LCM.

HCF(48, 18) × LCM(48, 18) = 48 × 18
Since the HCF of 48 and 18 = 6
⇒ 6 × LCM(48, 18) = 864
Therefore, LCM = 144
☛ HCF Calculator

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum