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Greatest Common Factor : Finding Made Easy - Lucid Explanation of an Efficient Method With Examples

In Elementary Number Theory, it is significant to find the largest positive integer that divides two or more numbers without remainder. For example it is useful for reducing vulgar fractions to be in lowest terms. To see an example, to reduce 203â... Read >

Binary Number System : Lucid Explanation of Conversion from and to Decimal Number System - Examples

The base-10 number system or decimal number system is the most popular system used by humans throughout the world. But, computers work internally with only two symbols, because of the straightforward implementation in digital electronic circuitry using... Read >

Quadratic Formula : Lucid Explanation of Its Derivation and Application in Solving Problems

Derivation of Quadratic formula : To solve ax^2 + bx + c = 0 where a ( ≠ 0 ), b, c are constants which can take real number values. ax^2 + bx + c = 0 or ax^2 + bx = -c Dividing by 'a' on both sides, we get x^2 + (b�a)x = -c�a or ... Read >

Prime Factorization of Natural Numbers : Lucid Explanation of the Method of Finding Prime Factors

Prime Factors : The factors of a natural number which are prime numbers are called the Prime Factors of that natural number. Examples : Factors of 8 are 1, 2, 4, 8. Out of these, only 2 is the Prime Factor. Also 8 = 2 x 2 x 2; Factor... Read >

Factoring Trinomials (Quadratics) : Lucid Explanation of the Method With Examples

Consider the product of the two linear expressions (y+a) and (y+b). (y+a)(y+b) = y(y+b) + a(y+b) = y^2 + by + ay + ab = y^2 + y(a+b) + ab We can write it as y^2 + y(a+b) + ab = (y+a)(y+b) .......(i) Similarly, Consider the product of the two l... Read >

Divisibility Rules for Prime Divisors

studying methods that can be used to determine whether a number is evenly divisible by other numbers, is an important topic in elementary number theory. These are shortcuts for testing a number's factors without resorting to division calculations. T... Read >

Modular Arithmetic (Congruences) Of Elementary Number Theory : Lucid Explanation With Examples

The eminent mathematician Gauss, who is considered as one of the greatest in history has quoted "mathematics is the queen of sciences and number theory is the queen of mathematics." Several important discoveries of Elementary Number Theory such as Ferm... Read >

Carrying out multiplication easily, speedily and executing mentally using Vedic Mathematics

There are methods, which are totally unconventional but help in Carrying out tedious and cumbersome arithmetical operations, easily, speedily and in some cases executing them mentally. People who are deeply rooted in the conventional methods, may find ... Read >

Algebra Word Problems

Equations are frequently used to solve practical problems. The steps involved in the method of solving an algebra word problem are as follows. STEP 1 : Read the problem carefully and note down what is given and what is required. ST... Read >