Q1
Euclid's division lemma is used to find the:
AHCF
BLCM
Csquare root
Dcube root
CBSEClass 10 (CBSE)MathematicsCh 1 · Topic 1
Euclid's Division Lemma and HCF
Learning to find the HCF of numbers using Euclid's division algorithm.
Core concept
To find the HCF of 96 and 404 using Euclid's algorithm: divide 404 by 96 (404=96×4+20), then divide 96 by the remainder 20 (96=20×4+16), continue dividing the previous divisor by the new remainder (20=16×1+4, then 16=4×4+0) — when the remainder becomes 0, the last non-zero remainder (4) is the HCF. This method is more efficient than listing all factors, especially for very large numbers.
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CBSE class 10 euclid's division lemma and hcf
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• Euclid's Division Lemma: a = bq + r, where 0 ≤ r < b.
• Euclid's algorithm repeatedly applies this lemma to find the HCF of two numbers.
• Continue dividing until the remainder is 0; the last non-zero remainder is the HCF.
• This method is more efficient than listing factors, especially for large numbers.