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How many multiples of 6 are between 100 and 1000?

 Oct 22, 2020
 #1
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(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, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600, 606, 612, 618, 624, 630, 636, 642, 648, 654, 660, 666, 672, 678, 684, 690, 696, 702, 708, 714, 720, 726, 732, 738, 744, 750, 756, 762, 768, 774, 780, 786, 792, 798, 804, 810, 816, 822, 828, 834, 840, 846, 852, 858, 864, 870, 876, 882, 888, 894, 900, 906, 912, 918, 924, 930, 936, 942, 948, 954, 960, 966, 972, 978, 984, 990, 996) Total = 150 such numbers

 Oct 22, 2020
 #2
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+1

Test theories with smaller numbers

 

eg  

How many multiples of 6 are between 10 and 50?  I have chosen numbers that are not multiples of 6 (like your question)

My guess is  (50-10)/6 = 6 and a bit.  So I am guessing 6 or  7

12,18, 24, 30, 36,42,48    It is 7 I had to round up.

 

Another example

How many multiples of 6 are between 10 and 40?  I have chosen numbers that are not multiples of 6 (like your question)

about (40-10)/6 = 5    That is spot on.

 

Now you tell me what your one will be.

 Oct 22, 2020

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