Divisors of 48

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

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: 485

 

What are Divisors of 48

A number n is a divisor of 48 if $\frac{48}{n}$ 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.

 

Key Things

The prime factorization of 48 is given below.

48 = 24 × 31

(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

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

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

$=31 \times 4=124$

(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

=4810/2

=485

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