Question

How many divisors (including 1, but excluding 1000) are there for the number 1000?

Answer 1

2 | 1000

2 | 500

2 | 250

5 | 125

5 | 5

| 1

1000= 2*2*2*5*5

follow above procedure to find number of divisors for any number including one and itself

in this process we use only prime numbers to divide a specific number until we get one as shown in picture

we can write 1000 as

(2^3)×(5^3) = 1000

for any number

'n' after primefactorization we get

n = (2^a)×(3^b)×(5^c)×(7^d)......

number of divisors for

n = (a+1)×(b+1) ×(c+1)........

similarly for

1000 = (3+1)×(3+1) = 16(including 1 and itself(1000))

excluding 1000 we get only 15