How to Find HCF of Two Numbers Using Prime Factorization and Division Method
H.C.F stands for Highest Common Factor. To find the H.C.F of two numbers we need to factorise the numbers and then take the common factors. After which we have to multiply the common factors and get the required H.C.F. In this article, you will get to know how to find HCF of two numbers, hcf of two numbers by division method and hcf of two numbers formula. To find the HCF by division method you will have to divide the larger number by the smaller number, until we get a remainder zero or unless further division is not possible.
H.C.F of Two Numbers
To find the HCF of any two numbers we need to follow the following steps:
Step 1: Take out the factors of the numbers. Let us suppose that the two numbers are 96 and 112.
Carrying Out HCF of 96 and 112
Step 2: Now we need to look at the common factors (C.F) of the numbers as shown below.
Carrying out HCF of 96 and 112
Step 3: We can see clearly the common factors highlighted in the colour blue. Now we will take the common factors from both the numbers and multiply them to get the HCF.
The HCF of 96 and 112 is 16
HCF of Two Numbers by Division Method
To find the HCF by division method you will have to divide the larger number by the smaller number and then again the remainder will become the divisor and divide the smaller number until we get a remainder zero or such that further division is not possible. Let’s practically understand this with the help of some examples.
Let us take two numbers, 46 and 242.
To find the HCF by division method we will divide the larger number by the smaller number.
HCF of 46 and 242
Hence, the required HCF of the numbers 46 and 242 is 2.
This method is also known as Euclid’s Division method named after the mathematician Euclid.
Let us consider a few more examples to understand the division method more clearly.
Solved Examples
Example 1: Find the H.C.F of 50 and 75.
Ans: First, you need to find the factors of the given numbers.
Step 1 of carrying out HCF of 50 and 75
After writing the factors then we will find the common factors. Here in this case the common factors are 5 and 5.
Step 2 of carrying out HCF of 50 and 75
After getting the common factors we will multiply the common factors to get the required H.C.F
HCF of 50 and 75 is 25
We can see clearly that the H.C.F of 50 and 75 is 25.
Example 2: Find the H.C.F of 432 and 876.
Ans: First, we need to find the factors of the given numbers.
Step 1 of carrying out HCF of 432 and 876
Now taking out the common factors from the factors above. We can see that the common factors are 2, 2 and 3.
Step 2 of carrying out HCF of 432 and 876
Now after multiplying the common factors we will get the required H.C.F of the given numbers.
The HCF of 432 and 876 is 12
Hence, the required H.C.F of the given numbers is 12.
Example 3: Find the HCF of 1334 and 8948.
Ans: We can see that the smaller number is 1334 and the larger number is 8948 so we will divide 8948 by 1334.
Here the smallest number which divides the dividend is 2 so we can say that the HCF of the given numbers 1334 and 8948 is 2.
Example 4: What is the highest common factor of 96 and 404?
Ans: Prime factorization of 96 = 2 × 2 × 2 × 2 × 2 × 3 = 25 × 3
Prime factorization of 404 = 2 × 2 × 101 = 22 × 101
HCF(96, 404) = 22 = 4
Therefore, the highest common factor of 96 and 404 is 4.
Practice Questions
Q 1 Find the H.C.F of 12, 45 and 75.
Ans: 3
Q 2 Find the H.C.F of 18,30 and 42.
Ans: 6
Q 3 Find the HCF of 867 and 255.
Ans: 51
Q 4 Find the HCF of 4052 and 12576.
Ans: 4
Summary
From HCF of two numbers examples, we have learnt to find the factors and then take the common factors. Then after that multiplication of the common factors will give us the HCF. We can use the division method to find the HCF. Hence, after going through this article we have made our concepts of HCF very clear in both methods and now we know how to find HCF of two numbers. With the examples and practice problem, we will get more clarity on the topic. So after reading the article go through the practice problem to have better understanding.
FAQs on HCF of Two Numbers Complete Concept Guide
1. What is the HCF of two numbers?
The HCF (Highest Common Factor) of two numbers is the greatest number that divides both numbers exactly without leaving a remainder.
- It is also called the GCD (Greatest Common Divisor).
- The HCF must be a common factor of both numbers.
- Among all common factors, it is the largest one.
- Example: The HCF of 12 and 18 is 6.
2. How do you find the HCF of two numbers?
You can find the HCF of two numbers using the listing method, prime factorization method, or division method.
- Listing method: Write all factors and choose the greatest common one.
- Prime factorization: Multiply common prime factors.
- Division (Euclidean) method: Divide repeatedly until remainder becomes 0.
3. What is the formula for HCF using prime factorization?
The HCF using prime factorization is found by multiplying the common prime factors with the smallest powers.
- Step 1: Write prime factorization of both numbers.
- Step 2: Identify common prime factors.
- Step 3: Multiply the common factors with least exponents.
- Example: 24 = 2³ × 3, 36 = 2² × 3² → HCF = 2² × 3 = 12.
4. How do you find the HCF using the division method?
The division method (Euclidean algorithm) finds the HCF by repeatedly dividing until the remainder is zero.
- Step 1: Divide the larger number by the smaller number.
- Step 2: Replace the larger number with the smaller number and the smaller number with the remainder.
- Step 3: Repeat until remainder = 0.
- The last non-zero divisor is the HCF.
5. What is the HCF of 12 and 18?
The HCF of 12 and 18 is 6.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common factors: 1, 2, 3, 6
- Greatest common factor = 6
6. What is the difference between HCF and LCM?
The HCF is the greatest common divisor of two numbers, while the LCM (Least Common Multiple) is the smallest common multiple.
- HCF deals with factors.
- LCM deals with multiples.
- Example: For 4 and 6, HCF = 2, LCM = 12.
7. Can the HCF of two numbers be 1?
Yes, the HCF of two numbers can be 1 if they are coprime numbers.
- Coprime numbers have no common factors other than 1.
- Example: 8 and 15 → HCF = 1.
- This means they share no common prime factors.
8. What is the HCF of two prime numbers?
The HCF of two different prime numbers is always 1.
- Prime numbers have only two factors: 1 and the number itself.
- Since they do not share common factors (except 1), HCF = 1.
- Example: 5 and 7 → HCF = 1.
9. What are the properties of HCF?
The HCF has important mathematical properties used in number theory.
- HCF of two numbers always divides both numbers exactly.
- HCF of a number with itself is the number.
- HCF of two coprime numbers is 1.
- HCF × LCM of two numbers = Product of the numbers.
10. How is HCF used in real life?
The HCF is used in real life to divide items into the largest equal groups without leftovers.
- Used in arranging objects into equal rows or groups.
- Helpful in simplifying fractions.
- Example: To divide 24 apples and 36 oranges into equal baskets, HCF = 12, so 12 baskets can be made.
