Divisors of 45

The divisors of 45 are those numbers that completely divide 45 without a remainder. In this section, we will discuss about divisors of 45.

Highlights of Divisors of 45

  • Divisors of 45: 1, 3, 5, 9, 15 and 45
  • Negative divisors of 45: -1, -3, -5, -9, -15 and -45
  • Prime divisors of 45: 3 and 5
  • Number of divisors of 45: 6
  • Sum of divisors of 45: 78
  • Product of divisors of 45: 453

 

What are Divisors of 45

A number n is a divisor of 45 if $\frac{45}{n}$ is an integer. Note that if 45/n=m is an integer, then both m and n will be the divisors of 45.

To find the divisors of 45, we need to find the numbers n such that 45/n becomes an integer. We have:

45/1=45 1, 45 are divisors of 45.
45/3=15 3, 15 are divisors of 45
45/5=9 5, 9 are divisors of 45

No numbers other than 1, 3, 5, 9, 15 and 45 can divide 45. So we conclude that

The divisors of 45 are:

1, 3, 5, 9, 15 and 45.

Thus, the total number of divisors of 45 is six.

 

Negative Divisors of 45

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 45 are 1, 3, 5, 9, 15, and 45, we can say that:

The negative divisors of 45 are -1, -3, -5, -9, -15, and –45.

 

Prime Divisors of 45

The divisors of 45 are 1, 3, 5, 9, 15, and 45. Among these numbers, only 3 and 5 are prime numbers. So we obtain that:

The prime divisors of 45 are 3 and 5.

 

Key Things

The prime factorization of 45 is given below.

45 = 3× 5

(i) By the number of divisors formula, we have that the number of divisors of 45 is

=(2+1)(1+1)=3×2=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 45 is

$=\frac{3^3-1}{3-1} \times \frac{5^2-1}{5-1}$

$=\frac{27-1}{2} \times \frac{25-1}{4}$

$=13 \times 6=78$

(iii) By the product of divisors formula, we have that the product of the divisors of 45 is

=45(Number of divisors of 45)/2

=456/2

=453

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