Nine of them.
6
332
334 of them.
There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine.
There are 142 of them.The 142th one is (7 x 142) = 994
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
666 integers.
There are 544 positive integers less than 1,000 that are either divisible by two or by 11.
6
8 of them.
332
130 numbers
334 of them.
To find how many positive integers less than 100 are divisible by 3, 5, and 7, we first calculate their least common multiple (LCM). The LCM of 3, 5, and 7 is 105. Since 105 is greater than 100, there are no positive integers less than 100 that are divisible by all three numbers. Therefore, the answer is 0.
To find how many positive integers less than or equal to 10,000 are divisible by 2, 5, or 10, we can use the principle of inclusion-exclusion. The count of integers divisible by each is: Divisible by 2: ( \frac{10000}{2} = 5000 ) Divisible by 5: ( \frac{10000}{5} = 2000 ) Divisible by 10: ( \frac{10000}{10} = 1000 ) Applying inclusion-exclusion, we have: [ 5000 + 2000 - 1000 = 6000 ] Thus, there are 6000 positive integers less than or equal to 10,000 that are divisible by 2, 5, or 10.
Except for 1, all of them.
There are 90 integers less than 1,000 that are divisible by 11.