Delving into the Secrets of Numbers

Prime Numbers

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. For example, 7 is prime because it’s only divisible by 1 and 7.

The first few prime numbers are 2, 3, 5, 7, 11, and so on. They form a fundamental building block in number theory.

Divisibility Rules

Divisibility rules provide shortcuts for determining if one number is divisible by another. For example, a number is divisible by 2 if its last digit is even.

The divisibility rule for 5 states that a number is divisible by 5 if its last digit is either 0 or 5.

If a % b == 0, then 'b' divides 'a'.

The Euclidean Algorithm

The Euclidean algorithm is an efficient method for finding the greatest common divisor (GCD) of two integers. It’s based on repeatedly applying the division algorithm.

Given two integers, a and b, with a > b: 1. Divide a by b and find the remainder r. 2. If r is 0, then GCD(a, b) = b. 3. Otherwise, replace a with b and b with r, and repeat step 1.

GCD(a, b) = GCD(b, a mod b)

Modular Arithmetic

Modular arithmetic deals with remainders after division. We use the modulo operator (%) to find the remainder of a division.

For example, 17 % 5 = 2 because 17 divided by 5 is 3 with a remainder of 2.

a mod b  ≡  (a - kb) mod b , where k is an integer.

Frequently asked questions

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