How to Find HCF of 3 Numbers Using Formula and Methods
The highest number that completely divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF) (GCD). The HCF of two numbers can be determined in a variety of methods. Using the prime factorization method is one of the easiest ways to get the HCF of two or more numbers. In this article, we will learn how to find HCF by long division method with some examples.
Steps to Find HCF of 3 Numbers by Using the Long Division Method
Follow the Steps for a better understanding:
Step 1: We first need to find out the HCF of the first two given numbers.
Step 2: Find out the HCF of the third number given and the HCF of the first two numbers that we got from the previous step.
Step 3: We mark the highest factor among which we found common.
Solved Examples
Q1. Find the HCF of 144, 198 and 162
Ans: Using the long division method
First of all, arrange the given numbers in ascending order. Not necessary but preferable.
Let's first find out the HCF of the first 2 numbers which are 144 and 198. i.e. HCF of 144 and 198.
HCF of 144 and 198 by Using Long Division Method
Therfore, the HCF of 144 and 198 = 18
The next step is to find the HCF of 162 and 18
HCF of 162 and 18
So by applying HCF division method, we get HCF of 162 and 18 = 18
Therefore the HCF of all the 3 numbers is
HCF of 144, 198 and 162 = 18
Note: It's Important that the Remainder is Always 0 at the End
Let's try to understand with one more example
Q2. Find the HCF of 729, 864 and 945
Ans: Using the long division method
Let's first find out the HCF of the first 2 numbers which are 729 and 864. i.e. HCF of 864 and 729.
HCF of 864 and 729
The HCF of HCF of 864 and 729 = 27
The next step is to find the HCF of the third number that is given which is 945 and the HCF of the first two numbers which is 27.
HCF of 945 and 27
HCF of 945 and 27 = 27
Therefore the HCF of all the 3 numbers is 27.
HCF of 729, 864 and 945 = 27
Practice Problem
Q1. Find the HCF of 30, 45 and 150
Ans: 15
Q2. Find the HCF of 126, 162 and 180
Ans: 18
Q3. Find the HCF of 300, 270 and 9
Ans: 3
Q4. Find the HCF of 78, 98 and 108
Ans: 2
Q5. Find the HCF of 702, 153 and 405
Ans: 9
Summary
This article has tried to explain the detailed steps of how to find HCF by using the long Division method for 3 given numbers. To find the HCF by division method the first step is to divide the larger number by the smaller number and then the remainder becomes the divisor and divide the smaller number until the remainder is zero. So, read the whole content nicely and do the solved examples present here in this article.
FAQs on HCF of 3 Numbers Explained with Steps and Examples
1. What is the HCF of 3 numbers?
The HCF (Highest Common Factor) of 3 numbers is the greatest number that exactly divides all three numbers without leaving a remainder. It is also called the Greatest Common Divisor (GCD).
- It must divide each of the three numbers completely.
- It is the largest among all common factors.
- Used to simplify ratios, fractions, and word problems.
2. How do you find the HCF of 3 numbers?
To find the HCF of 3 numbers, first find the HCF of any two numbers, then find the HCF of that result with the third number.
- Step 1: Find HCF of first two numbers.
- Step 2: Find HCF of the result and the third number.
- HCF(8, 12) = 4
- HCF(4, 16) = 4
3. What is the formula for HCF of 3 numbers?
The formula for the HCF of 3 numbers using LCM is: HCF × LCM = Product of the numbers (only for two numbers at a time). For three numbers, we usually apply:
- HCF(a, b, c) = HCF(HCF(a, b), c)
4. How do you find the HCF of 3 numbers using prime factorization?
To find the HCF of 3 numbers using prime factorization, multiply the common prime factors with the smallest powers.
- Step 1: Write prime factors of each number.
- Step 2: Identify common prime factors.
- Step 3: Multiply the lowest powers of common primes.
Common primes: 2¹ and 3¹
HCF = 2 × 3 = 6.
5. Can you give an example of HCF of 3 numbers?
Yes, the HCF of 15, 25, and 35 is 5.
- Factors of 15: 1, 3, 5, 15
- Factors of 25: 1, 5, 25
- Factors of 35: 1, 5, 7, 35
6. What is the difference between HCF and LCM of 3 numbers?
The HCF is the greatest number that divides all three numbers, while the LCM (Least Common Multiple) is the smallest number divisible by all three.
- HCF focuses on common factors.
- LCM focuses on common multiples.
- HCF ≤ LCM for positive integers.
7. What is the HCF of three prime numbers?
The HCF of three different prime numbers is 1 because prime numbers have no common factors except 1.
- Example: 3, 5, and 7
- Common factor = 1
8. What happens if one of the numbers is 0 while finding HCF of 3 numbers?
If one number is 0, the HCF of 3 numbers is the HCF of the remaining two non-zero numbers.
- HCF(a, b, 0) = HCF(a, b)
9. Is the HCF of 3 numbers always smaller than the numbers?
Yes, the HCF of 3 numbers is always less than or equal to the smallest number among them.
- It cannot exceed the smallest number.
- If all three numbers are equal, HCF equals that number.
10. Why is finding the HCF of 3 numbers important?
Finding the HCF of 3 numbers helps in simplifying ratios, reducing fractions, and solving real-life grouping problems.
- Used in dividing items into equal groups.
- Helps simplify algebraic expressions.
- Important in number theory concepts.
