HCF of 12 and 15

The HCF of 12 and 15 are any number that can divide both 12 and 15 entirely. Here the HCF of 12 and 15 is 3. There are different methods to find the HCF of the given numbers. Some methods focus on the prime factors and others on divisors.

Methods to find HCF

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

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HCF of 12 and 15 Using the Prime Factorization Method

To find the HCF using the prime factorization method the following steps are followed.

Step 1: Find the prime factors of the given number
Step 2: List the common prime numbers
Step 3: Multiply the common prime number. The result is the HCF of the number.
Therefore, the HCF of 12 and 15 is as follows:
Step 1: Find the prime factors of the given number
Prime factor of 12 = 2 × 2 × 3
Prime factor of 15 = 3 × 5 
Step 2: List the common prime numbers
The only common prime factor is 3
Step 3: Multiply the common prime number. The result is the HCF of the number.
Since 3 is the only prime number the multiplication step has not proceeded.
Hence, HCF(12,15) = 3

HCF of 12 and 15 Using the Long Division Method

To find the HCF using the long division method the following steps are carried out

Step 1: The larger number is divided by the smaller number until zero
Step 2: The last divisor is the HCF of the number
Therefore, the HCF of 12 and 15 using the long division method
Step 1: The larger number is divided by the smaller number until zero

Step 2: The last divisor is the HCF of the number
The last divisor is 3
Hence, the HCF(12,15) = 3

HCF of 12 and 15 Using the Listing Factor Method

Step 1: Find the factors of the given number
The factor of 12 = 1, 2, 3, 4, 6, and 12
The factor of 15 =1, 3, 5, and 15.
Step 2: Align the factors 
The common factors are only 1 and 3
Step 3: The highest common factor is the HCF of the number
The highest common factor is 3.
Hence, the HCF (12,15) = 3.

Solved Examples

Example 1: What are the HCF and LCM of 12 and 15?
The HCF of (12,15) = 3
The LCM of (12,15) = 60

Example 2: What is the HCF of 12 and 15 using the prime factorization method?
Prime factor of 12 = 2 × 2 × 3
Prime factor of 15 = 3 × 5 
The HCF of  (12,15) = 3

Example 3: If the product of two numbers is 180 and their HCF is 3. Find their LCM?
LCM×HCF = product of two numbers
LCM = product of two numbers  ∕  HCF
LCM = 180  ∕ 3
Hence LCM = 60.

Example 4:There are two numbers whose LCM and HCF are given find another number
LCM of the number = 60
HCF of the number = 3.
The number is given = 15
HCF (15,x) = 3
LCM(15,x) = 60
Therefore, LCM×HCF = (X)×15
 X = (LCM × HCF) ∕ 15
Hence, 
X = (3× 60)  ∕ 15
Therefore, X = 12 is the other number.

Example 5: What is the HCF of 12 and 15 if their LCM 60?
The HCF (12,15 ) = 3.

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Frequently Asked Questions (FAQ)

What is the LCM and HCF of 12 and 15, and find the product of 12 and 15?
The LCM of 12 and 15 = 60
The HCF of 12 and 15 = 3
The product of 12 and 15= 12✕15 = 180

Find the HCF of 12 and 15 by prime factorization.
Prime factor of 12 = 2 × 2 × 3
Prime factor of 15 = 3 × 5 
The HCF of  (12,15) = 3

Find the HCF of 867 and 225.
The HCF (867,225) = 3

Find the HCF of 12 and 15 by the division method.

HCF (12,15) = 3.

Find the HCF of 20 and 15.
The HCF (15,20) = 5.