Iterative division for HCF
Iterative division for HCF is a step-by-step method where the larger number is divided by the smaller number, then the divisor and remainder are used again until the remainder becomes 0. The last non-zero remainder is the HCF.
Practice This ConceptMain explanation
Teacher explanation
The HCF does not change when the larger number is replaced by the smaller number and the remainder. That is why the same logic can be used again and again, making the numbers smaller at every step. The method is fast and neat in exam work.
Example
For 252 and 198: 252 = 198 x 1 + 54, 198 = 54 x 3 + 36, 54 = 36 x 1 + 18, 36 = 18 x 2 + 0. So the HCF is 18.
Simple analogy
Keep the divisor, drop the old dividend, last non-zero wins.
Common confusion
Students stop after the first remainder or take the quotient instead of the last non-zero remainder.
Exam tip
Write each division clearly and stop only when the remainder becomes 0. The last non-zero remainder is the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of iterative division for hcf in one clean line.
2-mark use
Define iterative division for hcf and add one example or condition.
3-mark use
Explain iterative division for hcf, show the method or example, and mention the common mistake.
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