Real Numbers - Chapter Notes

Class 10 · CBSE · Mathematics · Real Numbers

Original notes on Euclid's division lemma, HCF, LCM and the Fundamental Theorem of Arithmetic for Class 10 Maths.

Euclid's division lemma

For positive integers a and b there exist unique integers q and r such that a = bq + r, where 0 <= r < b.

Finding HCF by Euclid's algorithm

• Divide the larger number by the smaller.
• Divide the divisor by the remainder.
• Repeat until the remainder is 0; the last divisor is the HCF.

Fundamental Theorem of Arithmetic

Every composite number can be written as a product of primes in exactly one way, apart from the order of the factors.

Useful result

For two positive integers a and b: HCF(a, b) x LCM(a, b) = a x b.

Example

Find HCF of 12 and 18. 18 = 12 x 1 + 6, then 12 = 6 x 2 + 0. So the HCF is 6.