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 $\dfrac{49}{n}$ 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.
Video solution of Divisors of 49:
Sum, Product & Number of Divisors of 49
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
$=\dfrac{7^3-1}{7-1}$
$=\dfrac{343-1}{6}=\dfrac{342}{6}$
$=57$
(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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