How many distinct prime factors does 100100 have?
To find out how many distinct prime factors 100100 has, we need to find the prime factorization of 100100 and count the number of unique prime factors.
First, let's find the prime factorization of 100100. We can start by dividing it by the smallest prime number, which is 2.
100100 ÷ 2 = 50050.
We continue dividing the quotient by 2 until we can no longer divide evenly:
50050 ÷ 2 = 25025.
Next, we divide the quotient by the next smallest prime number, which is 5:
25025 ÷ 5 = 5005.
Then, we divide the quotient by 5 again:
5005 ÷ 5 = 1001.
Finally, we divide the quotient by the next prime number, which is 7:
1001 ÷ 7 = 143.
At this point, we can stop because 143 is not divisible by any prime numbers greater than 7.
Now, let's write down the prime factorization of 100100:
100100 = 2 × 2 × 5 × 5 × 7 × 11.
We can see that there are 4 distinct prime factors: 2, 5, 7, and 11.
Therefore, the answer is that 100100 has 4 distinct prime factors.