Question

9973 is a prime number. Which of these is the sum of all the factors of 9973?

a) 9973
b) 9974
c) 9973 + 9973
d) (A prime number has no factors. So we cannot find the sum.)

Answer 1

Given:

9973 is a prime number

To Find:

Which of these is the sum of all the factors of 9973?

a) 9973

b) 9974

c) 9973 + 9973

d) (A prime number has no factors. So we cannot find the sum.)

Solution:

A prime number is a whole number that has only factors 1 and the number itself. The prime number should be greater than 1.

A factor is a number when multiplied with another number gives a number for which this number is a factor.

The sum of all factors of a number can be found by the formula,

Let the number be,

$N=2^a*3^b*5^c...$

Then the sum of factors will be represented by,

$Sum=(2^0+2^1+2^2+...)(3^0+3^1+3^2+...)(5^0+5^1+5^2+...)...$

Now the given number is 9973, the prime factorization for the number will be,

9973=1*9973

So the sum of factors will be,

$Sum=(9973^0+9973^1)\\=(1+9973)\\=9974$

Hence, the correct option is (b)9974.

Answer 2

Answer:

The correct option is (b) i.e. 9974.

Step-by-step explanation:

• In context to the given question, we have to find the sum of all the factors of 9973.

Given:

9973 is a prime number

Solution:

• We know that :

• A prime number is a whole number that has only factors 1 and the number itself. The prime number should be greater than 1.

therefore:

Factors of prime number 9973 = 9973 and 1

Now, as we have to find the sum of factor of 9974

The sum of factors will be :

= 9973 + 1

= 9974

Hence, the correct option is (b) i.e. 9974.