102, 108, 114, 120, 126, 132, 138, 144, and 150
There are 29 numbers between 1 and 150 that are divisible by five.
150/8 = 18.75 so 18 numbers.
150 ÷ 9 = 16 r 6 → the first natural number between 150 and 300 divisible by 9 is 9 × 17 (=154)300 ÷ 9 = 33 r 3 → the last natural number between 150 and 300 divisible by 9 is 9 × 33 (=297)→ there are 33 - 17 + 1 = 17 natural numbers between 150 and 300 divisible by 9.
10 numbers
20 of them.
126
There are (500-100)/2 = 200 numbers divisible by 2 between 100 and 500 counting 100 but not 500. Of these (500-100)/8 = 50 are divisible by 8. So there are 150 numbers between 100 and 500 divisible by two but not by 8. By relative primeness exactly 50 out of these 150 are divisible by 3 and therefore these 50 are exactly the ones divisible by 6 but not by 8.
There are 29 numbers between 1 and 150 that are divisible by five.
To find how many numbers between 1 and 300 are divisible by 3 or 4, we can use the principle of inclusion-exclusion. The count of numbers divisible by 3 is ( \lfloor 300/3 \rfloor = 100 ), and those divisible by 4 is ( \lfloor 300/4 \rfloor = 75 ). The numbers divisible by both (i.e., by 12) are ( \lfloor 300/12 \rfloor = 25 ). Thus, the total count is ( 100 + 75 - 25 = 150 ). Therefore, there are 150 numbers between 1 and 300 that are divisible by either 3 or 4.
Every 6th number beginning with 102. There are 150 of them, and the last one is 996.
150/8 = 18.75 so 18 numbers.
150 ÷ 9 = 16 r 6 → the first natural number between 150 and 300 divisible by 9 is 9 × 17 (=154)300 ÷ 9 = 33 r 3 → the last natural number between 150 and 300 divisible by 9 is 9 × 33 (=297)→ there are 33 - 17 + 1 = 17 natural numbers between 150 and 300 divisible by 9.
10 numbers
150
There are 600 5-digit numbers divisible by 150.
20 of them.
There are 899 numbers between 100 and 1000. Every 6th number is divisible by 6. 899 divided by 6 is 149 and 5/6. The answer must be 149 or 150. The first number in that set is 102 (17 x 6). The last is 996 (166 x 6). 166 - 17 + 1 is 150. There are 150 numbers between 100 and 1000 that are divisible by 6.