The divisors of 48 are those numbers that completely divide 48 without a remainder. In this section, we will discuss about divisors of 48.

Table of Contents

## Highlights of Divisors of 48

- Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
- Negative divisors of 48: -1, -2, -3, -4, -6, -8, -12, -16, -24 and -48
- Prime divisors of 48: 2 and 3
- Number of divisors of 48: 10
- Sum of divisors of 48: 124
- Product of divisors of 48: 48
^{5}

## What are Divisors of 48

A number n is a divisor of 48 if $\dfrac{48}{n}$ is an integer. Note that if 48/n=m is an integer, then both m and n will be the divisors of 48.

To find the divisors of 48, we need to find the numbers n such that 48/n becomes an integer. We have:

48/1=48 | 1, 48 are divisors of 48. |

48/2=24 | 2, 24 are divisors of 48 |

48/3=16 | 3, 16 are divisors of 48 |

48/4=12 | 4, 12 are divisors of 48 |

48/6=8 | 6, 8 are divisors of 48 |

No numbers other than 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 can divide 48. So we conclude that

The divisors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. |

Thus, the total number of divisors of 48 is ten. See that 24 is the biggest proper divisor of 48.

## Negative Divisors of 48

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

As the divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, we can say that:

The negative divisors of 48 are -1, -2, -3, -4, -6, -8, -12, -16, -24, and –48.

## Prime Divisors of 48

The divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 48 are 2 and 3.

Video solution of Divisors of 48:

## Sum, Product & Number of Divisors of 48

The prime factorization of 48 is given below.

48 = 2^{4 }× 3^{1}

(i) By the number of divisors formula, we have that the number of divisors of 48 is

=(4+1)(1+1)=5×2=10.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 48 is

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

$=\dfrac{32-1}{1} \times \dfrac{9-1}{2}$

$=31 \times 4=124$

(iii) By the product of divisors formula, we have that the product of the divisors of 48 is

=48^{(Number of divisors of 48)/2}

=48^{10}^{/2}

=48^{5}

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