Find the H.C.F by Euclid Algorithm by using color ribbon or grid paper.
What we have learnt
Division Algorithm: Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ t < b.
The Fundamental Theorem Of Arithmetic states that every composite number can be expressed (factorized) as a product of its primes and this factorization is unique, apart from the order in which the prime factors occur.
If p is a prime and p divides a2, where a is a positive integer , then p divides a.
Let x be a rational number whose decimal expansion terminates.Then we can express x in the form of p ÷ q ,p and q are coprimes anf the factorization of q is of the form 2 n5 m,where n and m are non-negative integers.
Let x = p ÷ q be a rational number such that the prime factorization of q is of the form of 2n 5 m, where n and m are non-negative integers. Then x has a decimal expansion which terminates.
Let x = p ÷q be a rational number such that the prime factorization of q is not of the form of 2 n5m, where n and m are non-negative integers.Then x has a decimal expansion which is non-terminating and repeating (recurring).
We define log a x = n, if a n = x, where a and x are positive numbers and a ≠ 1.
Laws of Logarithms :
If a, x and y are positive real numbers and a ≠ 1, then
log a xy = log a x + log ay
log a x ÷ y = log ax − log a y
log a x m = m log a x
a log a N = N
log a 1 = 0
log a a = 1
Logarithms are used for caluculations in engineering, science, business and economics.
