What is Long Division Method for HCF?

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Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Long Division Method for HCF (Highest Common Factor) is a systematic way to find the largest number that divides two or more numbers exactly, without leaving a remainder. It involves repeatedly dividing the larger number by the smaller number until the remainder becomes zero. The last non-zero divisor is the HCF.

Simple Example

Quick Example

Imagine you have 12 ladoos and 18 jalebis. You want to pack them into identical boxes, with each box having the same number of ladoos and the same number of jalebis, without mixing them. The HCF of 12 and 18 will tell you the maximum number of boxes you can make, ensuring no sweets are left over.

Worked Example

Step-by-Step

Let's find the HCF of 48 and 60 using the Long Division Method.

Step 1: Divide the larger number (60) by the smaller number (48).
60 ÷ 48 = 1 with a remainder of 12.

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Step 2: Now, take the divisor (48) and the remainder (12). Divide the divisor (48) by the remainder (12).
48 ÷ 12 = 4 with a remainder of 0.

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Step 3: Since the remainder is now 0, the last non-zero divisor is our HCF.

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So, the HCF of 48 and 60 is 12.

Why It Matters

Understanding HCF is crucial in fields like Computer Science for optimizing code and in Cryptography for securing digital information. Engineers use it when designing systems that need to fit together perfectly, and even in Data Science, it helps in simplifying complex ratios. It's a foundational skill for future innovators!

Common Mistakes

MISTAKE: Stopping the division too early, before the remainder becomes zero. | CORRECTION: Continue dividing the previous divisor by the new remainder until the remainder is exactly 0.

MISTAKE: Confusing the HCF with the quotient or the first remainder. | CORRECTION: The HCF is always the *last divisor* when the remainder becomes zero.

MISTAKE: Starting with the smaller number as the dividend in the first step. | CORRECTION: Always divide the *larger* number by the *smaller* number in the first step.

Practice Questions

Try It Yourself

QUESTION: Find the HCF of 25 and 35. | ANSWER: 5

QUESTION: What is the HCF of 72 and 108? | ANSWER: 36

QUESTION: A class has 36 boys and 45 girls. The teacher wants to divide them into equal groups for a project, with each group having only boys or only girls. What is the largest possible number of students in each group? | ANSWER: 9

MCQ

Quick Quiz

Which of the following is the HCF of 16 and 24?

The Correct Answer Is:

Using the long division method: 24 divided by 16 gives a remainder of 8. Then, 16 divided by 8 gives a remainder of 0. The last divisor is 8, so the HCF is 8.

Real World Connection

In the Real World

In India, HCF is used in everyday situations like a tailor cutting cloth. If a tailor has two pieces of fabric, one 120 cm long and another 180 cm long, and wants to cut them into the largest possible equal-sized strips without any waste, they would find the HCF of 120 and 180. This tells them each strip should be 60 cm long.

Key Vocabulary

Key Terms

HCF: Highest Common Factor, the largest number that divides two or more numbers exactly. | Divisor: The number by which another number is divided. | Dividend: The number being divided. | Remainder: The amount left over after division. | Quotient: The result obtained by dividing one number by another.

What's Next

What to Learn Next

Great job learning about HCF! Next, you can explore the 'Least Common Multiple (LCM)' which is another important concept related to factors and multiples. Understanding both HCF and LCM will help you solve many real-world problems more easily.