### HCF of 825, 675, and 450

**HCF of 825, 675, and 450**: The highest Common Factor or HCF of a number is found by considering the numbers that are larger and are common in all the given numbers. The HCF mainly involves knowing the factors of the numbers and not the multiples. All the factors are taken into account and the highest common factor is the HCF. An example could be considering that “x” and “z” are two numbers for which you need to find the HCF. The factors that are common in both the numbers are written first, the highest factor that was common in both the numbers is the HCF of x and z.

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**What Is the HCF Of 825, 675, and 450?**

There are different methods to find the HCF using simple steps.

- Listing Factor Method
- Prime Factorization Method
- Division Method

**HCF Of 825, 675, and 450 Using the Listing Factor Method**

The listing factor method is carried out by aligning the factors making a list of the factors and finding the HCF.

Step 1: Find the factors and list them

Step 2: The highest common factor is the HCF

Therefore, the HCF of 825, 675, and 450 using the factor method

Step 1: Find the factors and list them

Factor of 825 = 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

Factor of 675 = 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

Factor of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Step 2: The highest common factor is the HCF

The highest common factor is 75

Hence, HCF(825,675,450) = 75.

**HCF Of 825, 675, and 450 Using the Prime Factorization Method**

Prime factorization is finding HCF using only prime factors and not all the factors. The steps are as follows:

Step 1: Find the prime factors

Step 2: Multiply the common highest prime number, the product is the HCF of the number.

Therefore, the HCF of 825, 675, and 450 using the prime factorization method is as follows:

Example 1: Find the HCF of 825, 675, and 450 using the prime factor method

Step 1: Find the prime factors

The prime of 825 = 3✕5✕11

The prime factor of 675 = 3✕3✕3✕5✕5

The prime factor of 450 = 2✕3✕3✕5✕5

Step 2: Multiply the common highest prime number, the product is the HCF of the number.

The common highest prime factors = 3✕5✕5

Hence the HCF (825,675,450) = 75

**HCF Of 825, 675, and 450 Using the Long Division Method**

The long division method is one of the easiest simple and most commonly used methods to find the HCF of the numbers. This method was also used in competitive exams to save time. The steps are as follows:

Step 1: The larger number is divided by the smaller number

Step 2: The last divisor is the HCF of the number

Therefore, the HCF of 825, 675, and 450 using the long division method is as follows:

Example 1: Find the HCF of 825, 675, and 450 using the long division method

Step 1: The larger number is divided by the smaller number

Step 2: The last divisor is the HCF of the number

The last divisor is the number 75

Hence, HCF (825,675,450) = 75

**Solved Examples:**

**Example 1: What is the greatest number that divides 825,675 and 450 equally?**

The greatest or the highest number that divides 825, 675, and 450 equally = 75

**Example 2: What is the second HCF of 825,675 and 450?**

The second HCF of 825, 675, and 450 = 25.

**Example 3: What is the LCM of 825, 675, and 450 if their HCF is 75?**

The LCM of (825, 675 and 450) = 14850 if their HCF is 75.

**Example 4: What is the HCF of the following numbers 825, 675, and 450?**

The HCF (825,675,450)) = 75

**Example 5: What is the GCD of 825,675 and 450 if their LCM is 14850?**

The GCD of (825,675,450) = 75

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**Frequently Asked Question (FAQ)**

**Are the LCM and HCF of 825,675, and 450 the same?**

No, the LCM and HCF of 825, 675, and 450 are different. Their LCM = 14850 and their HCF = 75

**Find the HCF of 825, 675, and 450 using the division method?**

The HCF (825,675,450) = 75.

**How to Find the HCF of 825, 675, and 450 by Prime Factorization?**

The prime of 825 = 3✕5✕11

The prime factor of 675 = 3✕3✕3✕5✕5

The prime factor of 450 = 2✕3✕3✕5✕5

Hence HCF (825,675,450) =75.

**What are the common multiples of 825, 675, and 450?**

The common multiples of 825,675 and 450 are 75,150 and 225.

**Is there any real-time application of HCF?**

Yes, HCF finds its real-time application in the world for organizing, dividing, and categorizing things for events or for any occasion.

**What are the common prime factors of 825, 675,450?**

The common prime factor of 825,625 and 450 are 3 and 5.

Written by

Prerit Jain