In the realm of mathematics, mastering the concept of Highest Common Factor (HCF) is paramount for students in Class 4. HCF, also known as Greatest Common Divisor (GCD), plays a crucial role in solving arithmetic problems and forms the foundation for more advanced mathematical concepts. This comprehensive guide for Class 4 students will delve into the intricate world of HCF, equipping them with a solid understanding and problem-solving prowess.
HCF, or GCD, is the largest number that divides two or more numbers without leaving a remainder. For instance, the HCF of 12 and 18 is 6, as it is the largest number that divides both 12 and 18 evenly.
HCF holds immense significance in various mathematical operations:
There are two primary methods to determine the HCF:
This method involves factoring each number into its prime factors and identifying the common factors. The product of these common factors is the HCF.
The division method repeatedly divides the larger number by the smaller number until the remainder becomes 0. The last non-zero remainder is the HCF.
Example 1: Find the HCF of 12 and 18 using the factorization method.
Solution:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Common factors: 2 × 3
HCF = 2 × 3 = 6
Example 2: Find the HCF of 24, 36, and 48 using the division method.
Solution:
36 ÷ 24 = 1 R 12
24 ÷ 12 = 2 R 0
HCF = 12
Numbers | Factorization | HCF |
---|---|---|
12, 18 | 2 × 2 × 3, 2 × 3 × 3 | 6 |
24, 36, 48 | 2 × 2 × 2 × 3, 2 × 2 × 3 × 3, 2 × 2 × 2 × 2 × 3 | 12 |
15, 25, 35 | 3 × 5, 5 × 5, 7 × 5 | 5 |
Pros:
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Mastering HCF sums is essential for success in Class 4 mathematics. By understanding the concept thoroughly, applying effective strategies, and avoiding common mistakes, students can enhance their problem-solving abilities and set the stage for future academic achievements. Embrace the challenge of HCF sums and strive for mathematical excellence!
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