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