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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