# Divisors of 24

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

#### Highlights of Divisors of 24

• Divisors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
• Negative divisors of 24: -1, -2, -3, -4, -6, -8, -12 and -24
• Prime divisors of 24: 2 and 3
• Number of divisors of 24: 8
• Sum of divisors of 24: 60
• Product of divisors of 24: 244

#### What are Divisors of 24

A number n is a divisor of 24 if $\frac{24}{n}$ 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:

 24/1=24 1, 24 are divisors of 24. 24/2=12 2, 12 are divisors of 24 24/3=8 3, 8 are divisors of 24 24/4=6 4, 6 are divisors of 24

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.

#### Negative Divisors of 24

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.

#### Prime Divisors of 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.

Key Things

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

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

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

$=15 \times 4=60$

(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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