How would I find the smallest three digit number that is divisible by exactly three different prime numbers? My friend says the answer is 2 - 3 - 17 but won't tell me how he got it. Any help would be much appreciated. Thank You.
THIS IS NOT HELPING ME!!!!;;
the 3 smallest primes are 2,3,5.
So, 2*3*5=30 is the smallest number divisible by 3 primes.
But we want a 3-digit number
100 = 2^2 * 5 - nope only 2 primes
101 is prime - only one prime divisor
102 = 2*3*17 - we have a winner!
To find the smallest three-digit number that is divisible by exactly three different prime numbers, you need to identify the three smallest prime numbers and check their multiples until you find a number that is greater than or equal to 100.
The three smallest prime numbers are 2, 3, and 5. To find the smallest three-digit number divisible by these three primes, you can start by finding the multiples of 2, then 2 * 3, and finally 2 * 3 * 5.
Let's go step by step:
1. Multiples of 2: Start with the smallest number, 2, and keep adding 2 until you find a number that is greater than or equal to 100.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100.
The smallest multiple of 2 that is greater than or equal to 100 is 100.
2. Multiples of 2 * 3: Now, start with the number we found in the first step, 100, and keep adding 2 * 3 until you find a number greater than or equal to 100.
100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200.
The smallest multiple of 2 * 3 that is greater than or equal to 100 is 102.
3. Multiples of 2 * 3 * 5: Lastly, start with the number found in the second step, 102, and keep adding 2 * 3 * 5 until you find a number greater than or equal to 100.
102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300.
The smallest multiple of 2 * 3 * 5 that is greater than or equal to 100 is 102.
Therefore, the smallest three-digit number that is divisible by exactly three different prime numbers (2, 3, and 5) is 102.
Your friend is incorrect in stating that the answer is 2 - 3 - 17.