What are the DIVISORS of 45

From a PROFESSOR we bring a new math lesson, in this case what are the divisors of 45. For them, we will see the meaning and characteristics of divisibility. Then we review their criteria and prime numbers. Finally, we will see what are the dividers of 45 specifically.

When we talk about divisibility in mathematics, we say that one number is divisible by another if or only if its division is exact, that is, it has no remainder or, in other words, its remainder is equal to zero.

Divisibility is the property that numbers have to divide and dividing means being able to separate the total of something into equal parts. The difference between division and divisibility is that the latter has a result that is exact and can be measured, while division is for any number and sometimes cannot be measured.

In mathematics, divisibility refers to the property of integers, that is, numbers without decimals, to be divided by another integer and that its result is also an integer.

We use the arithmetic operation DIVISION to divide, which is composed of a dividend and a divisor, being the first the number of parts that we want to know that go into the total, and the second is the number of the total that we want split.

The divisors of a number will be all those numbers that can divide exactly that number. The number one and the number itself are always divisors, that is, each number is divisible by itself and by one.

Divisibility Properties

The properties that we must take into account about divisibility are:

• Divisible numbers can only be composed of integers that are all nonzero.
• All numbers are divisible by themselves and one.

45 is NOT a prime number, then the number 45 is a composite number. On the other hand we see that the number 45 ends in 5 and its digits add up to 9, which is a multiple of 3.

Therefore we can say that 45 is divisible by 3, 5 and 9.

So:

• 45 / 3 = 15
• 45 / 5 = 9
• 45 / 9 = 5
• 45 / 15 = 3

Therefore we say that the divisors of 45 are: 1 - 3 - 5 - 9 - 15 - 45.

The number 45 has 6 divisors.

The divisibility rules They help us to know if one number is divisible by another, without the need to carry out a division.

• A number is divisible by 2 if it ends in a zero or an even number. Examples: 40 - 882 - 2316
• A number is divisible by 3 if its digits or the sum of its digits is a multiple of three. Examples: 9 - 81 - 333
• A number is divisible by 4 if the last two digits are a number divisible by 4. Examples: 112 - 3020
• A number is divisible by 5 if it ends in 0 or 5. Examples: 55 - 170
• A number is divisible by 6 if the number is divisible by 2 and 3. Examples: 36 - 114
• A number is divisible by 7 if double is applied to the last digit and the difference between the rest of the number, and the result is equal to zero or divisible by 7. Examples: 49 - 672
• A number is divisible by 8 if the last three digits are a number divisible by 8. Examples: 64 - 216 - 109816
• A number is divisible by 9 if the sum of the digits is divisible by 9. Examples: 27 - 1629
• A number is divisible by 10 if it ends in zero. Examples: 20 - 890 - 12480

We can also perform the decomposition into Prime numbers, to be able to determine the divisors of a number. In the divisibility criteria to decompose a number, we reduce that number into its prime factors.

A prime number is an integer greater than zero. which has exactly two dividers. These numbers are only divisible by themselves and by the number 1, which is NOT considered a prime number.

There is the Fundamental Theorem of Arithmetic which states that every integer occurs uniquely as a product of prime numbers. Prime numbers are considered to be “firsts”. Derived from the Latin "primus" means first, since the other integers are obtained from them.

The Sieve of Eratosthenes

The Eratosthenes Sieve is a procedure that is used to determine all prime numbers up to a given natural number, generally up to 100. To do this, a table of numbers is traversed using the following procedure:

First we cross out the number 1 since we know that it is not a prime number.

Then we are going to continue with the number 2, so the number 2 is “highlighted” as the first prime number. Then we are going to "cross out" all the numbers that are multiples of 2, such as 4, 6, 8, 10, etc.

To continue, we see in the table and the next number not crossed out is 3, therefore we highlight it as a prime and cross out all the multiples of 3, such as 9.15, etc.

The next number not crossed out is the 5 that we are going to highlight as the next prime number, thus crossing out all the multiples of 5, such as 25, 35, etc.

We continue with 7 and highlight it as a prime, crossing out all the multiples of 7. And we carry out this same process until completing the table reaching the number 100.

In this way we will find all the prime numbers from 1 to 100.

Composed numbers

The composed numbers are those non-prime numbers, with the exception of 1, that have one or more divisors other than 1 and itself.

Examples: 4 - 6 - 8 - 9 - 10 - 12 ….

Now yes, we can see what the divisors of 45 are.