Question

I am a two digit composite odd number I am a multiple of 9 and the sum of my divisor is 104 who am I​

Answer 1

Answer:

I am 63

Step-by-step explanation:

Since 104 is not a large number we can do it by trial and error method

Multiple of 9 are 18, 27, 36, 45, 54, 63

Since the number is odd, we should start from 27

sum of divisors of 27 = 1 + 3 + 9 + 27 = 40

Again taking 45

sum of divisors of 45 = 1 + 3 + 5 + 15 + 45 = 69

again taking 63

sum of divisors of 63 = (7²-1)/(7-1) × (3³-1)/(3-1) = 8 × 13 = 104

Therefore, the number is 63

Note: In the end a formula for finding the sum of divisors is used since its difficult to calculate sum of all the divisors by writing it down

Formula to calculate the sum of divisors

If $p_1^a$ and  $p_2^b$ are relatively prime and any number A can be written as

$A=p_1^a \times p_2^b$

Then the sum of the divisors of A is

$\frac{(p_1^{a+1}-1)}{(p_1-1)} \times \frac{(p_2^{b+1}-1)}{(p_2-1)}$

Answer 2

Answer:

9

Step-by-step explanation:

Composite Numbers before 10: 4, 6, 8, and 9

The only one of those 4 that is NOT a multiple of 2: 9