HCF of 867 and 225

The HCF of 867 and 225 are any numbers that can divide both 867 and 225 entirely. Here the HCF of 867 and 225 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 are as follows:

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

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HCF of 867 and 225 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 867 and 225 using the prime factorization method is as given below:
Step 1: Find the prime factors of the given number
Prime factor of 867 = 3 × 17 × 17
Prime factor of 225 = 3 × 3 × 5 × 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(867,225) = 3

HCF of 867 and 225 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 867 and 225 using the long division method is as given below:
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(867,225) = 3

HCF of 867 and 225 Using the Listing Factor Method

To find the HCF using the listing factor method the following steps are followed

Step 1: Find the factors of the given number
Step 2: Align the factors 
Step 3: The highest common factor is the HCF of the number
Therefore, the HCF of 867 and 225 using the listing factor method is as given below:
Step 1: Find the factors of the given number
The factor of 867 = 1, 3, 17, 51, 289, 867
The factor of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
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(867,225) = 3.

Solved Examples:

Example 1: What are the HCF and LCM of 867 and 225?
The HCF of (867,225) = 3
The LCM of (867,225) = 65025

Example 2: What is the HCF of 867 and 225 using the prime factorization method?
Prime factor of 867 = 3 × 17 × 17
Prime factor of 225 = 3 × 3 × 5 × 5
The HCF of  (867,225) = 3

Example 3: what is the HCF of 867 and 225 using the listing factor method
The factor of 867 = 1, 3, 17, 51, 289, 867
The factor of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
The HCF(867,225) = 3.

Example 4: Find the HCF of 12 and 15
The factor of 12 = 1, 2, 3, 4, 6, and 12
The factor of 15 =1, 3, 5, and 15.
Hence, the HCF(12,15) = 3

Example 5: What is the HCF of 867 and 225 if their LCM 65025?
The HCF (867,225 ) = 3.

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Frequently Asked Questions (FAQ)

What are the LCM and HCF of 867 and 225?
The LCM of 867 and 225 = 65025
The HCF of 867 and 225 = 3

Find the HCF of 867 and 225 by prime factorization.
Prime factor of 867 = 3 × 17 × 17
Prime factor of 225 = 3 × 3 × 5 × 5
The HCF of  (867,225) = 3

Find the HCF of 12 and 15.
The HCF (12,15) = 3

Find the HCF of 867 and 225 by the division method.

HCF (867,225) = 3.

What is HCF?
HCF is the highest common factor or the greatest common divisor that divides any number equally.