Divisors of 24 - Mathstoon

The divisors of 24 are those numbers that completely divide 24 without a remainder. In this section, we will discuss about divisors of 24.

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Highlights of Divisors of 24

A number n is a divisor of 24 if $\dfrac{24}{n}$ is an integer. Note that if 24/n=m is an integer, then both m and n will be the divisors of 24.

To find the divisors of 24, we need to find the numbers n such that 24/n becomes an integer. We have:

No numbers other than 1, 2, 3, 4, 6, 8, 12, and 24 can divide 24. So we conclude that

The divisors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24.

Thus, the total number of divisors of 24 is eight.

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

As the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, we can say that:

The negative divisors of 24 are -1, -2, -3, -4, -6, -8, -12, and –24.

The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 24 are 2 and 3.

Video solution of Divisors of 24:

The prime factorization of 24 is given below.

24 = 2³× 3¹

(i) By the number of divisors formula, we have that the number of divisors of 24 is

=(3+1)(1+1)=4×2=8.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 24 is

$=\dfrac{2^4-1}{2-1} \times \dfrac{3^2-1}{3-1}$

$=\dfrac{16-1}{1} \times \dfrac{9-1}{2}$

$=15 \times 4=60$

(iii) By the product of divisors formula, we have that the product of the divisors of 24 is

=24^{(Number of divisors of 24)/2}

=24⁸^/2

=24⁴

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