the NCF or two positive integerse and h, with abis obtained as follow
Step 1 Apply the division lemma to find a and where ab 7.0 b.
Continue the process till the remainder is zero. The divisor at this stage
Every composite number can be expressed (factorised) as a product of primes, and
2. Buclid's division algorithm. This is based on Euclid
Stepsr-the HCF is apply Euclid's lemma to band
Step 3:
HCF(.). Also, HCF. b) HCF).
3. The Fundamental Theorem of Arithmetic
factorisation is unique, apart from the order in which the prime factors occur
4. If pis a prime and p divides a', then p divides a, where a is a positive integer
5. To prove that 2.5 are irrationals
6. Let a be a rational mumber whose decimal expansion terminates. Then we can expres
in the form where p and q are coprime, and the prime factorisation of q is of the
205". where n. m are non-negative integers.
7. Letx=be a rational number, such that the prime factorisation of q is of the form 29
where n. m are non-negative integers. Then x has a decimal expansion which terminar
8. Letzl be a rational number, such that the prime factorisation of g is not of the for
2* 5 where , mare non-negative integers. Then x has a decimal expansion which
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