Divisibility
An inexhaustible source of arithmetic wonders, divisibility criteria are far from all being known… and even farther from being mastered! Everyone knows how to recognize an integer divisible by 2, 3, 5, 9 or 10 or by one of their products. Divisibility by 11 is already a bit less familiar. But what about divisibility by prime numbers such as 13, 17, 19, 23 or 29? You're stumped? Yet there are simple tricks that make it possible to develop criteria for each of them. As early as the 17th century, Pascal had developed some to help merchants. Other original algorithms continue to thrive today, such as those of Vosburgh Lyons.
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Finding divisors... without dividing
Telling almost at a glance whether one integer is divisible by another can sometimes be quite a challenge. Yet there are perfectly reliable ways to do so, even with fairly large numbers!
Pascal's ribbons
In the past, arithmetic mattered as much to merchants and accountants as it did to scholars. In the 17th century, Blaise Pascal devised a method for automatically testing whether one integer is divisible by another.
When 60 divides 9
Divisibility can be considered in sets of numbers other than the integers. One such set, introduced as early as fourth grade, lends itself perfectly to this generalization: the terminating decimals.
Magical divisibility tests: maths and conjuring | Tangente
The mathemagician sometimes uses divisibility to dazzle the audience. Before turning to the solutions, try to work out for yourself the mathematics behind the tricks that follow. Amaze your friends with magic while doing mathematics!
Divide and conquer: divisibility tests in action | Tangente
Many arithmetic problems can be solved using standard methods, whether elementary or advanced. But some puzzles call for a basic concept—divisibility—and a little ingenuity.