Number System Important terms, theorems etc.
Lemma
A Lemma is a proven statement used for providing another statement.
Euclid's Division Lemma
Given two positive integers a and b, a > b there exists unique integers q and r satisfying a = bq + r, 0 < = r < b.
Euclid's Division algorithm
This is used to obtain the HCF of two positive integers, say a and b, with a > b, follow the steps below:
# Apply Euclid's division lemma, to a and b. So, we find whole numbers, q and r such that a = bq + r, 0 < = r < b.# If r = 0, b is the HCF of a and b. If r not equal to 0, apply the division lemma to b and r.
# Continue the process till the remainder is zero. the divisor at this stage will be the required HCF.
4.05.2008
Prime Numbers
A number which has exactly two factors. example 2, 3, 5.
Composite Numbers
A number which has more than two factors. Example 4, 6, 8.
Is 1 a prime number?
No. 1 is neither prime nor composite because it has only 1 factor.
16.05.2008
Is Every whole/integer no. rational ?
Yes, because every whole no. can be written with denominator 1 that is in the form of p/q where p and q are integers and q is not equal to zero.
examples 3 = 3/1, - 9 = - 9/1
Is Every rational no. a whole/integer no. ?
No. 7/5 is a rational number but not a whole no./ integer.
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