How many positive integers less than 100 and divisible by 3 are also divisible by 4?
To determine how many positive integers less than 100 are divisible by both 3 and 4, we need to find the common multiples of 3 and 4.
Step 1: Find the multiples of 3 less than 100.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57,
60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96.
Step 2: Find the multiples of 4 less than 100.
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96.
Step 3: Identify the numbers that appear in both lists.
The common multiples of 3 and 4 less than 100 are 12, 24, 36, 48, 60, 72, 84, and 96.
Step 4: Count the common multiples.
There are a total of 8 positive integers less than 100 that are divisible by both 3 and 4.
Therefore, there are 8 positive integers less than 100 that are divisible by both 3 and 4.
To find out how many positive integers less than 100 are divisible by both 3 and 4, we need to find the multiples of both 3 and 4 within the range.
Step 1: Find the multiples of 3 less than 100.
To find the multiples of 3, we start with 3 and keep adding 3 until we reach a number greater than or equal to 100.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ..., 99
Step 2: Identify the multiples of 4 within this list.
We can see that the multiples of 4 are: 12, 24, 36, 48, 60, 72, 84, 96.
Step 3: Count the number of multiples of 3 that are also multiples of 4.
Counting these numbers, we have 8 positive integers that are less than 100, divisible by 3, and divisible by 4 - 12, 24, 36, 48, 60, 72, 84, 96.
Therefore, there are 8 positive integers less than 100 that are divisible by both 3 and 4.