8 junio, 2024

Divisors of 8: what are they and easy explanation

What are the divisors of 8?

The divisors of 9 are 1, 2, 4 and 8.

How to know? We divide by integers less than 8, so that the result is an integer:

How to calculate the divisors of 8?

The divisors of 8 are all those integers that, when divided by 8 among themselves, the result is also an integer less than 8.

Another way of defining them is as follows: an integer «m» is a divisor of 8 if when 8 is divided by «m» (8÷m), the remainder or remainder of said division is equal to 0.

The decomposition of a number into prime factors is obtained by dividing the number by the prime numbers less than this.

To determine which are the divisors of 8, the number 8 is first broken down into prime factors, where it is obtained that 8=2³=2*2*2.

This indicates that the only prime factor that 8 has is 2, but this is repeated 3 times.

How are divisors obtained?

Having done the decomposition into prime factors, we proceed to calculate all the possible products between those prime factors.

In the case of 8, there is only one prime factor, which is 2, but it is repeated 3 times. Therefore, the divisors of 8 are: 2, 2*2 and 2*2*2. That is: the divisors of 8 are 1, 2, 4, 8.

To the previous list it is necessary to add the number 1, since 1 is always a divisor of any integer. Therefore, the list of divisors of 8 so far is: {1, 2, 4, 8}.

Are there more divisors?

The answer to this question is yes. But which divisors are missing?

According to what was said before, all the divisors of a number are the possible products between the prime factors of said number.

But it was also indicated that the divisors of 8 are all those integers, such that when dividing 8 among them, the remainder of the division is equal to 0.

The last definition speaks of integers in general, not just positive integers. Therefore, it is also necessary to add the negative integers that divide 8.

The negative integers that divide 8 are the same as those found previously, with the difference that the sign will be negative. That is, -1, -2, -4 and -8 must be added.

With what has been said before, it can be concluded that all the divisors of 8 are: {±1, ±2, ±4, ±8}.

Observation

The definition of divisors of a number is limited to integers only. Otherwise, it could also be said that 1/2 divides 8, since when dividing between 1/2 and 8 (8÷1/2), the result is 16, which is an integer.

The method presented in this article to find the divisors of the number 8 can be applied to any whole number.

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