Question

The number of distinct prime factors of the largest 4 digit number is
A. 2
B. 3
C. 5
D. 11

Answer 1

Hint: Factor is also known as divisor of a number. A prime number is a number which has only 2 factors, 1 and the number itself. Prime factors are the factors which are primes. The largest 4 digit number is 9999. So find the prime factors and count the distinct ones.

Complete step-by-step answer:
We are given to find the number of distinct prime factors of the largest 4 digit number.
The largest 4 digit number is 9999 as its next number 10000 which is a 5 digit number.
9999 is an odd number so it is not divisible by the smallest prime number 2.
The next prime number of 2 is 3.
9999 can be written as three times 3333.
 $ 9999 = 3 \times 3333 $
3333 can also be written as three times 1111.
$3333 = 3 \times 1111 $
 $\Rightarrow 9999 = 3 \times 3 \times 1111 $
1111 is not divisible by 3 and the next primes of 3 are 5, 7. 1111 is not divisible by 5 and 7.
The next prime number is 11.
1111 is divisible by 11 and 1111 can also be written as 101 times 11.
 $ 1111 = 11 \times 101 $
 $ \Rightarrow 9999 = 3 \times 3 \times 11 \times 101 $
And 101 is a prime number so we cannot further divide it.
Therefore the distinct prime factors of 9999 are 3, 11 and 101. No. of distinct prime factors is 3.
So, the correct answer is “3”.

Note: Normal factors include both prime and non-prime (composite) numbers including 1. No. of factors of a number is always greater than the no. of prime factors, because 1 is a factor of every number and 1 is not prime. Distinct means different from others.