### 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.

Written by by

Prerit Jain