# Divisors of 49

The divisors of 49 are those numbers that completely divide 49 with the remainder zero. In this section, we will discuss about divisors of 49.

#### Highlights of Divisors of 49

• Divisors of 49: 1, 7 and 49
• Negative divisors of 49: -1, -7 and -49
• Prime divisors of 49: 7
• Number of divisors of 49: 3
• Sum of divisors of 49: 57
• Product of divisors of 49: 493/2 =73=343.

#### What are Divisors of 49

A number n is a divisor of 49 if $\frac{49}{n}$ is an integer. Note that if 49/n=m is an integer, then both m and n will be the divisors of 49.

To find the divisors of 49, we need to find the numbers n such that 49/n becomes an integer. We have:

 49/1=49 1, 49 are divisors of 49. 49/7=7 7 is a divisor of 49

No numbers other than 1, 7 and 49 can divide 49. So we conclude that

 The divisors of 49 are: 1, 7 and 49.

Thus, the total number of divisors of 49 is three.

#### Negative Divisors of 49

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

As the divisors of 49 are 1, 7, and 49, we can say that:

The negative divisors of 49 are -1, -7, and –49.

#### Prime Divisors of 49

The divisors of 49 are 1, 7, and 49. Among these numbers, only 7 is a prime number. So we obtain that:

The only prime divisor of 49 is 7.

Key Things

The prime factorization of 49 is given below.

49 = 72

(i) By the number of divisors formula, we have that the number of divisors of 49 is

=(2+1)=3.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 49 is

$=\frac{7^3-1}{7-1}$

$=\frac{343-1}{6}=\frac{342}{6}$

$=57$

(iii) By the product of divisors formula, we have that the product of the divisors of 49 is

=49(Number of divisors of 49)/2

=493/2

=73

=343

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