HIGHEST COMMON FACTOR HCF
Definition Of Highest Common Factor (HCF)
The Highest Common Factor (HCF) of two or more numbers is the highest number that divides the numbers exactly.
More About Highest Common Factor (HCF)
If the highest common factor (HCF) of two numbers is equal to 1, then they are called co-prime or relatively prime.
The product of the highest common factor (HCF) and the lowest common multiple (LCM) of two numbers is equal to the product of the numbers.
Example of Highest Common Factor (HCF)
To find the HCF of 12, 24, and 36, first we list out the factors of the three numbers.
12 - 1, 2, 3, 4, 6, and 12
24 -1, 2, 3, 4, 6, 8, 12, and 24
36 - 1, 2, 3, 4, 6, 8, 12, 18, and 36
So, the HCF of the numbers 12, 24, and 36 is 12.
Video Examples: Highest Common Factor (HCF)
In another method we need to write all the prime factors of the three numbers 12, 24, and 36.
12 - 2 × 2 × 3
24 - 2 × 2 × 2 × 3
36 - 2 × 2 × 3 × 3
Then we list out all the common prime factors. The common prime factors of the three numbers are 2 × 2 × 3.
Then we have to multiply the common prime factors.
2 × 2 × 3 = 12
So, the HCF of the three numbers 12, 24, and 36 is 12.
Solved Example on Highest Common Factor (HCF)
Ques: Find the HCF of 18 and 35.
Choices:
A. 1
B. 5
C. 7
D. 9
Correct Answer: A
Solution:
Step 1: 18 = 1, 2, 3, 6, 9, and 18 [List the factors of 18.]
Step 2: 35 = 1, 5, 7, and 35 [List the factors of 35.]
Step 3: The common factor of 18 and 35 is 1.
Step 4: So, the HCF of 18 and 35 is 1.
Quick Summary
- HCF is the largest number that divides two or more numbers without leaving a remainder.
- If the HCF of two numbers is 1, they are co-prime or relatively prime.
- The product of HCF and LCM of two numbers equals the product of the numbers.
🍎 Teacher Insights
Use real-world examples to illustrate the concept of HCF, such as dividing objects into equal groups. Emphasize the connection between factors and HCF.🎓 Prerequisites
- Factors
- Multiples
- Divisibility
Check Your Knowledge
Q1: What is the HCF of 12 and 18?
Q2: The HCF of two numbers is 1. What are these numbers called?
Frequently Asked Questions
Q: What is the difference between HCF and LCM?
A: HCF is the highest number that divides the given numbers exactly, while LCM is the lowest number that is divisible by all the given numbers.
Q: How do you find the HCF of more than two numbers?
A: You can list the factors of each number and identify the highest factor common to all, or use prime factorization.