The HCF of 825, 675 and 450 is 75. HCF is the greatest integer that can divide 825, 675 and 450 evenly. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers, there would be common factors, and the highest among the common factors is known as the HCF. In the given set of numbers 825, 675 and 450, the common factors are 1, 3, 5, 15, 25 and 75. Since 75 is the highest among the common factors, HCF would be 75 for 825, 675 and 450. HCF is also termed as GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 825, 675 and 450?
The Highest Common Factor, also known as the Greatest Common Factor, of 825, 675 and 450 is 75.
How to Find HCF of 825, 675 and 450?
There are three methods to find the HCF of 825, 675 and 450:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 825, 675 and 450 by Prime Factorisation Method
In the Prime Factorisation, the numbers can be expressed as the product of prime numbers. Here, 825, 675 and 450 can be expressed as;
825 = 3 × 5 × 5 × 11
675 = 3 × 3 × 3 × 5 × 5
450 = 2 × 3 × 3 × 5 × 5
Common Prime Factors are 3 × 5 × 5. Therefore, HCF will be,
HCF (825, 675 and 450) = 3 × 5 × 5 = 75.
HCF of 825, 675 and 450 by Long Division Method
In the Long division method, the following steps are followed.
- Choose two numbers from the given set of numbers (Usually, the first two numbers are selected).
- From the chosen numbers, the smallest number becomes the Divisor, and the larger number becomes the Dividend.
- In the next step, the smaller number becomes the Dividend, and the remainder becomes the Divisor.
- The above step is followed until the remainder is zero.
- The last Divisor would be the HCF.
- The HCF and the left-out number are taken for a new long division.
- HCF becomes the Divisor, and the other number becomes the Dividend.
- Long Division is continued until the remainder becomes zero.
- The last Divisor is the HCF of all the three numbers.
HCF of 825, 675 and 450 by the Long Division method is;
Stage 1: Choosing 825 and 675 for 1st Long Division, the HCF would be 75
Stage 2: Choosing HCF and next number for Long Division.
i.e. HCF from previous Long Division = 75 and left out number is 450. Again the HCF is 75.
The Division is shown below;
Therefore, HCF (825, 675 and 450) = 75
HCF of 825, 675 and 450 by Listing the Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 825, 675 and 450:
Factors of 825:
1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
Factors of 675:
1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
Factors of 450:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Therefore, HCF (825, 675 and 450) = 75
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the Greatest number that divides 825, 675 and 450 evenly.
The Greatest number that divides 825, 675 and 450 evenly is nothing but the GCF, which is 75.
2. What is the second HCF for 825, 675 and 450?
The second HCF for 825, 675 and 450 is 25.
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