Page 5 - Matematica_Mathematics - Divizibilitatea_Divisibility

We write a b and read a divide by b or a is a multiple of b (a divides exactly by b). The same we can
note b | a, we read B divide a or b is a divisor of a.
12 3, we read 12 divide by 3 or 12 is a multiple of 3.

3 | 12, we read 3 divide it (that is, divide it into equal parts) on the 12th or 3 is divisor of 12.

You can see that the number of divisors is finite, while the number of multiples of a natural number is
infinite.
But how can we find out all the divisors of a natural number?

Let’s take the number 42 as an example. Since it is an even number, we know for sure that it divides by 2.
42 = 1 × 42
42 = 2 × 21
21 = 3 × 7

So, 1, 2, 3 and 7 are divisors of 42. Now we will “play” with these dividers, to find out the others.

2 3 7

2 × 3, 2 × 7, 3 × 7 and 2 × 3 × 7, respectively 6, 21 and 42 are divisors of 42.

Practice

2. Do you have a favorite number? Find out its divisors and some of the multiples.

Did you In the year 585 B.C., using the divisibility properties of
know...? numbers, Thales of Miletus (636 - 546 B.C.) predicted a solar eclipse.