How many distinct prime factors does 100100 have?
To find the number of distinct prime factors of a given number, you need to first prime factorize the number, which involves breaking it down into its prime factors.
Let's start with 100100. We can divide it by the smallest prime number, 2.
100100 ÷ 2 = 50050
Now we continue dividing by 2 until we can't anymore:
50050 ÷ 2 = 25025
Next, we divide by the next prime number, 3:
25025 ÷ 3 = 8341
We proceed with dividing by 5:
8341 ÷ 5 = 1668.2 (approximately)
Since 1668.2 is not a whole number, we move on to the next prime number, 7:
8341 ÷ 7 = 1191.6 (approximately)
Continuing with division by 7:
1191.6 ÷ 7 = 170.2 (approximately)
Finally, we divide by 11:
170.2 ÷ 11 = 15.47 (approximately)
At this point, we stop because 15.47 is not a prime number. By now, we have completed the prime factorization of 100100, which is:
100100 = 2^2 * 5^2 * 7 * 11
Therefore, 100100 has a total of four distinct prime factors: 2, 5, 7, and 11.