How many distinct prime factors does 100100 have?
collecting cans and bottles for recycling. the ratio is 8 cans to 9 bottles. If you collected 240 cans how many items did you collect in all. Explain to me how you get the answer, please!
2 square* 5 square* 7* 11* 13 = 100100
So, the distinct prime factors are 5.
To determine the number of distinct prime factors of a given number, we need to find all the prime numbers that divide the number without leaving a remainder.
To do this, we start by prime factorizing the given number, 100100.
First, we divide it by the smallest prime number, 2.
100100 / 2 = 50050
Next, we try dividing the quotient, 50050, by 2 again:
50050 / 2 = 25025
As we can see, 2 does not divide 25025 without leaving a remainder. So, we move on to the next prime number, which is 3.
25025 / 3 = 8341.67
Again, 3 does not divide 8341.67 without leaving a remainder. So, we try the next prime number, which is 5.
8341.67 is not divisible by 5, so we move on to the next prime number, which is 7.
8341.67 / 7 = 1191.667
Here, we can see that 7 divides 1191.667 without leaving a remainder. So, we continue dividing the quotient by 7.
1191.667 / 7 = 170.2381
Again, we divide the quotient, 170.2381, by 7:
170.2381 / 7 = 24.31973
Finally, we can see that 7 divides 24.31973 without leaving a remainder. Now, we try dividing the quotient by 7 one more time:
24.31973 / 7 = 3.47424
At this point, we can observe that 7 no longer divides the number without leaving a remainder.
So, we have found all the prime factors that divide 100100 without remainder, and they are 2, 5, and 7.
Therefore, the number 100100 has three distinct prime factors: 2, 5, and 7.