HCF of 12 and 18

The HCF of 12 and 18 is 6. The greatest integer that can divide the numbers 12 and 18 evenly is called the highest common factor. The methods that are widely used to find the HCF of the number are:

• Listing Factor Method
• Long Division Method
• Prime Factorization Method.

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HCF of 12 and 18 Using the Long Division Method

The HCF using the long division method is obtained by dividing the larger number by a smaller number. The divisor is usually taken as the HCF of the number.

Step 1: Divide the greater digit by a smaller digit
Step 2: The last divisor from which zero is obtained is the HCF of the number.
Therefore, the HCF of 12 and 18 using the long division method is as given below:
Step 1: Divide the greater digit by a smaller digit

Step 2: The last divisor from which zero is obtained is the HCF of the number.
The corresponding divisor is 6.
Hence the HCF(12,18) = 6.

HCF of 12 and 18 Using the Prime Factorization Method

Prime factors are any numbers but not 1. They are the factors of 1 and themselves. Finding the prime numbers for the given number will give the HCF of the number.

Step 1: Find the prime factors of the given numbers
Step 2: List the common prime factors
Step 3: Multiply the common prime factors which are the HCF of the given numbers. 
Therefore, the HCF of 12 and 18 using the prime factorization method is as given below:
Step 1: Find the prime factors of the given numbers
The prime factors of 12 = 2 × 2 × 3
The prime factors of 18 = 2 × 3 × 3
Step 2: List the common prime factors
The common prime factors =  2 × 3
Step 3: Multiply the common prime factors which are the HCF of the given numbers. 
 By multiplying the common prime numbers we get 6
Hence, HCF(12,18) = 6.

HCF of 12 and 18 Using the Listing Factor Method

By listing the factors of the given numbers and finding the common factors the HCF of the number can be determined using the listing factor method

Step 1: Find the factors and list the common factors
Step 2: The largest factor that is common is the HCF of the given number.
Therefore, the HCF of 12 and 18 using the listing factor method is as given below:
Step 1: Find the factors and list the common factors
The factors of 12 = 1, 2, 3, 4, 6, 12
The factors of 18 = 1, 2, 3, 6, 9, 18
The common factors are 1,2,3 and 6
Step 2: The largest factor that is common is the HCF of the given number.
The factor that is the largest among the four factors is 6.
Hence, HCF(12,18) = 6

Solved Examples:

Example 1: What are the HCF and LCM of 12 and 18?
The HCF of (12,18) = 6
The LCM of (12,18) = 36

Example 2: What is the HCF of 12 and 18 using the prime factorization method?
The prime factors of 12 = 2 × 2 × 3
The prime factors of 18 = 2 × 3 × 3
The HCF of  (12,18) = 6

Example 3: If the product of two numbers is 216 and their HCF is 6. Find their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 216  ∕ 6
Hence LCM = 36.

Example 4:There are two numbers whose LCM and HCF are given find another number
LCM of the number = 36
HCF of the number = 6.
The number is given = 12
HCF (12,x) = 6
LCM(12,x) = 36
Therefore, LCM×HCF = (X)×12
 X = (LCM × HCF) ∕ 12
Hence, 
X = (6× 36)  ∕ 12
Therefore, X = 18 is the other number.

Example 5: What is the HCF of 12 and 18 if their LCM 36?
The HCF (12,18 ) = 6.

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Frequently Asked Questions (FAQ)

What is the LCM and HCF of 12 and 18, and find the product of 12 and 15?
The LCM of 12 and 18 = 36
The HCF of 12 and 18 = 6
The product of 12 and 18= 12✕18 = 210

Find the HCF of 12 and 18 by the listing factor method.
The factors of 12 = 1, 2, 3, 4, 6, 12
The factors of 18 = 1, 2, 3, 6, 9, 18
The HCF of  (12,18) = 6

Find the HCF of 56 and 84.
The HCF (56,84) = 28

Find the HCF of 12 and 18 by the division method.

HCF (12,18) = 6.