Prime factors
They are prime numbers which are factors of a given number. e.g., Prime factors of 42 = 2 x 3 x..
Prime numbers
It can only be divided by one or itself i.e., a prime number has no factors other than 1 and itself. e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, are examples of prime numbers..
Rational and Irrational Numbers
Introduction - The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecuti..
Question 3
Question: What is a prime number? Answer: A number which has only two factors, namely 1 and then number itself is called a prime number..
Illustrative Examples
Example 1: - 01. If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not tru..
Illustrative Examples
The following are the Illustrative Examples: If P(n) is the statement n 2 -n+41 is prime, prove that P(1), P(2) are true but P(41) is not true. Prove by P.M.I , n < 2 n for all n ..
Common factor
A number which is a factor of two or more numbers is called a common factor of these numbers. e.g., 4 is a common factor of 16 and ..
Factor Theorem
Statement - If p(x), a polynomial in x is divided by x-a and the remainder = f (a) is zero, then (x-a) is a factor of p(..
Factor Theorem
If p(x), a polynomial in x is divided by x-a and the remainder = f (a) is zero, then (x-a) is a factor of p(x..
Divisibility, Divisors or Factors and Multiples,
If a number has a whole number answer when divided by a second number, the first number is divisible by the second number; x is divisible by y if and only if x = qy where y is a whole number. A multiple is the product of any quant..
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