# Divisors of 50

The divisors of 50 are those numbers that completely divide 50 without a remainder. In this section, we will discuss about divisors of 50.

#### Highlights of Divisors of 50

• Divisors of 50: 1, 2, 5, 10, 25 and 50
• Negative divisors of 50: -1, -2, -5, -10, -25 and -50
• Prime divisors of 50: 2 and 5
• Number of divisors of 50: 6
• Sum of divisors of 50: 93
• Product of divisors of 50: 503

#### What are Divisors of 50

A number n is a divisor of 50 if $\frac{50}{n}$ is an integer. Note that if 50/n=m is an integer, then both m and n will be the divisors of 50.

To find the divisors of 50, we need to find the numbers n such that 50/n becomes an integer. We have:

 50/1=50 1, 50 are divisors of 50. 50/2=25 2, 25 are divisors of 50 50/5=10 5, 10 are divisors of 50

No numbers other than 1, 2, 5, 10, 25 and 50 can divide 50. So we conclude that

 The divisors of 50 are: 1, 2, 5, 10, 25 and 50.

Thus, the total number of divisors of 50 is six.

#### Negative Divisors of 50

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

As the divisors of 50 are 1, 2, 5, 10, 25, and 50, we can say that:

The negative divisors of 50 are -1, -2, -5, -10, -25, and –50.

#### Prime Divisors of 50

The divisors of 50 are 1, 2, 5, 10, 25, and 50. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:

The prime divisors of 50 are 2 and 5.

Key Things

The prime factorization of 50 is given below.

50 = 21 × 52

(i) By the number of divisors formula, we have that the number of divisors of 50 is

=(1+1)(2+1)=2×3=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 50 is

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

$=\frac{4-1}{1} \times \frac{125-1}{4}$

$=3 \times 31=93$

(iii) By the product of divisors formula, we have that the product of the divisors of 50 is

=50(Number of divisors of 50)/2

=506/2

=503

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