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What is the Long Division Method for HCF?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The Long Division Method for HCF is a step-by-step process to find the Highest Common Factor (HCF) of two or more numbers. It uses repeated division until the remainder becomes zero. The last non-zero divisor is the HCF.
Simple Example
Quick Example
Imagine you have two cricket teams, Team A scored 48 runs and Team B scored 60 runs. If you want to find the largest number of equal groups you can make for both scores (like for dividing sweets equally among fans), you would use the HCF. The long division method helps you find this largest common number.
Worked Example
Step-by-Step
Let's find the HCF of 24 and 36 using the Long Division Method.
Step 1: Divide the larger number (36) by the smaller number (24).
36 ÷ 24 = 1 with a remainder of 12.
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Step 2: Now, the remainder (12) becomes the new divisor, and the previous divisor (24) becomes the new dividend.
24 ÷ 12 = 2 with a remainder of 0.
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Step 3: Since the remainder is now 0, the last divisor (12) is the HCF.
So, the HCF of 24 and 36 is 12.
Why It Matters
Understanding HCF is super important for many cool fields! In Computer Science, it helps in simplifying fractions used in coding. In Cryptography, HCF concepts are used to create secure codes that protect your online messages and banking. It's also a basic building block for engineers designing things efficiently.
Common Mistakes
MISTAKE: Students sometimes stop dividing when the first remainder appears, thinking it's the HCF. | CORRECTION: You must continue dividing until the remainder becomes zero. The HCF is the *last* non-zero divisor.
MISTAKE: Swapping the divisor and dividend incorrectly in subsequent steps, especially when the remainder is larger than the previous divisor. | CORRECTION: Always make the previous divisor the new dividend and the current remainder the new divisor.
MISTAKE: Forgetting to divide the larger number by the smaller number first. | CORRECTION: Always start by dividing the larger number by the smaller number. If there are three numbers, find the HCF of two first, then find the HCF of that result and the third number.
Practice Questions
Try It Yourself
QUESTION: Find the HCF of 18 and 45 using the Long Division Method. | ANSWER: 9
QUESTION: What is the HCF of 56 and 84? Show your steps. | ANSWER: 28
QUESTION: Three friends want to share 30 laddoos and 42 jalebis equally among themselves, such that each person gets the same number of each sweet. What is the maximum number of friends they can invite to share the sweets equally? (Hint: Find the HCF of 30 and 42) | ANSWER: 6
MCQ
Quick Quiz
Which number is the HCF when using the Long Division Method?
The first divisor
The first remainder
The last non-zero divisor
The final remainder
The Correct Answer Is:
C
The HCF in the long division method is always the last non-zero divisor. Options A and B are incorrect because the process continues, and option D is incorrect because the final remainder is always zero.
Real World Connection
In the Real World
Imagine you are a textile shop owner in India, and you have two rolls of fabric, one 120 cm long and another 180 cm long. You want to cut both rolls into pieces of equal length, as long as possible, without any waste. Using the Long Division Method for HCF helps you find the maximum length of each piece, which would be 60 cm in this case, making your cutting efficient!
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 that is being divided. | Remainder: The amount left over after division. | Quotient: The result of division.
What's Next
What to Learn Next
Great job learning HCF! Next, you should explore the 'Least Common Multiple (LCM)' concept. LCM and HCF are like two sides of the same coin and are often used together to solve many math problems, especially with fractions.
