HCF of 12 and 18

HCF of 12 and 18 is 6. HCF stands for Highest Common Factor, which is the largest positive integer that can divide two or more numbers without leaving any remainder. Finding the HCF of two numbers is useful for simplifying fractions, solving equations, and finding common multiples.

In this article, we will learn how to find the HCF of 12 and 18 by three different methods: prime factorization, long division, and listing common factors.

What is HCF?

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), refers to the largest positive integer that divides two or more numbers without leaving a remainder.

Some examples of HCF are:

• For the numbers 12 and 15, the HCF is 3, as 3 is the largest number that divides both 12 and 15 without leaving a remainder.
• For the numbers 18 and 24, the HCF is 6, as 6 is the largest number that divides both 18 and 24 without leaving a remainder.

What is HCF of 12 and 18?

Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of 12 and 18 is the largest positive integer that divides both numbers without leaving a remainder.

In this case, the HCF of 12 and 18 is 6. This result can be found by factoring each number into their prime factors and looking for common ones among them:

12 = 2 × 2 × 3 and 18 = 2 × 3 × 3.

The common factor between these two expressions is 2 × 3 = 6. Therefore, the HCF of 12 and 18 is 6.

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How to Find HCF of 12 and 18?

HCF of 12 and 18 can be founded by following methods:

• Prime Factorization
• Listing Multiples
• Euclid’s Division Method

Let’s discuss these methods in detail as follows.

HCF of 12 and 18 by Prime Factorization

Prime factorization involves breaking down each number into its prime factors and HCF of 12 and 18 can be calculated using Prime factorization as follows:

Step 1: Write the prime factorization of 12 and 18 as follows:

12 = 2 × 2 × 3 and 18 = 2 × 3 × 3

Step 2: Identify the common prime factors of 12 and 18. In this case, they are 2 and 3.

Step 3: Multiply the common prime factors to get the HCF. Therefore, the HCF of 12 and 18 is:

HCF(12, 18) = 2 × 3 = 6

Thus, HCF of 12 and 18 is 6.

Learn more about, Prime Factorization Method

HCF of 12 and 18 by Listing Factors

Steps for HCF of 12 and 18 by Listing Factors is given as follows:

Step 1: List all the factors of each number 12 and 18

• Factors of number 12 = 1, 2, 3, 4, 6, 12
• Factors of number 18 = 1, 2, 3, 6, 9, 18

Step 2: Identify the common prime factors:

For 12 and 18, the common factors are 1, 2, 3, and 6.

Step 3: Highest common factor is HCF.

Among the common factors, 6 stands as the highest common factor.

Thus, HCF of 12 and 18 by listing factors is 6.

HCF of 12 and 18 by Euclid Division Algorithm

Steps to find HCF of 12 and 18 by Euclid Division Algorithm are:

Step 1: Start with the given numbers: a = 12 and b = 18.

Step 2: Apply Euclid’s division lemma.

18 = 12 · 1 + 6

Here, q = 1 and r = 6.

Step 3: Now, replace a with b and b with r:

a = 12 (new value of a) and b = 6 (new value of b)

Step 4: Repeat the process until remainder is 0.

: [ 12 = 6 · 2 + 0 ] Here, q = 2 and r = 0.

Since the remainder is 0, we stop here.

For 12 and 18, applying long division yields an HCF of 6.

HCF vs LCM of 12 and 18

While HCF represents the largest factor common to both numbers, the Least Common Multiple (LCM) denotes the smallest multiple that is divisible by both numbers.

Metric	HCF (12, 18)	LCM (12, 18)
Definition	The largest positive integer that is a factor of both 12 and 18.	The smallest positive integer that is a multiple of both 12 and 18.
Value	6	36
Interpretation	The largest number that can exactly divide both 12 and 18.	The smallest number that is both a multiple of 12 and 18.

FAQs on HCF of 12 and 18

Define HCF.

Highest Common Factor (HCF), also known simply as the greatest common divisor or greatest common denominator, refers to the largest positive integer that divides two given integers without leaving any remainder.

What is LCM?

Least Common Multiple (LCM) of two integers is the smallest positive multiple that is divisible by both numbers.

What is the LCM of 12 and 18?

LCM of 12 and 18 is 36.

Is HCF(12, 18) greater than LCM(12, 18)?

As HCF(12, 18) = 6 and LCM(12, 18) = 36.

Thus, HCF (12, 18) is not greater than LCM(12, 18).

What is the Relationship between HCF and LCM?

For any two number x and y relationships between HCF and LCM is: HCF(x, y) × LCM(x, y) = xy.

How to Calculate HCF?

There are many methods to calculate HCF i.e.,

• Prime Factorization
• Listing Multiples
• Euclid’s Division Method