There are 67 numbers between 100 and 500 divisible by 6. The first number greater than 100 divisible by 6: 100 ÷ 6 = 16 r 4 → first number divisible by 6 is 6 × 17 = 102 Last number less than 500 divisible by 6: 500 ÷ 6 = 83 r 2 → last number divisible by 6 is 6 × 83 = 498 → all multiples of 6 between 17 × 6 and 83 × 6 inclusive are the numbers between 100 and 500 that are divisible by 6. → there are 83 - 17 + 1 = 67 such numbers.
There are 232 numbers between 1 and 500 that are divisible by 3 or 5.
There are 43 natural numbers between 200 and 500 that are divisible by seven.
Which of these numbers is closest to 500?
Exclusively, meaning not including 200 and 500, there are 149 even (divisible by two) numbers between 200 and 500.
There are 67 numbers between 100 and 500 divisible by 6. The first number greater than 100 divisible by 6: 100 ÷ 6 = 16 r 4 → first number divisible by 6 is 6 × 17 = 102 Last number less than 500 divisible by 6: 500 ÷ 6 = 83 r 2 → last number divisible by 6 is 6 × 83 = 498 → all multiples of 6 between 17 × 6 and 83 × 6 inclusive are the numbers between 100 and 500 that are divisible by 6. → there are 83 - 17 + 1 = 67 such numbers.
There are 63 numbers 1 to 500 that are divisible by six but not by eight.
There are 232 numbers between 1 and 500 that are divisible by 3 or 5.
There are 43 natural numbers between 200 and 500 that are divisible by seven.
Which of these numbers is closest to 500?
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Exclusively, meaning not including 200 and 500, there are 149 even (divisible by two) numbers between 200 and 500.
Just divide 500 / 9 = 55.55555... ; so there are 55 numbers in the range divisible by 9. Here they are:918273645546372819099108117126135144153162171180189198207216225234243252261270279288297306315324333342351360369378387396405414423432441450459468477486495
500 numbers are divisible by 2.
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 is no limitation given to the number of digits in the number, thus: For 3 digit numbers: to be less than 500 the first digit can be only one of {1, 2, 3, 4} leading to 4 × 5 × 4 = 80 numbers For 2 digit numbers: they are all less than 500, and there are 6 × 5 = 30 numbers For 1 digit numbers: they are all less than 500, and there are 6 numbers Thus there are in total 80 + 30 + 6 = 116 numbers that can be made form the digits {1, 2, 3, 4, 5 ,6} without repetitions that are less than 500.
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