# SOLUTION: Hi. Can someone please teach me how to solve this question? It's quite easy but I want to know how. It would mean a lot. Thanks! How many integers between 197 and 303 are divis

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Hi. Can someone please teach me how to solve this question? It's quite easy but I want to know how. It would mean a lot. Thanks! How many integers between 197 and 303 are divis      Log On

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 Algebra: Divisibility and Prime Numbers Solvers Lessons Answers archive Quiz In Depth

 Question 597022: Hi. Can someone please teach me how to solve this question? It's quite easy but I want to know how. It would mean a lot. Thanks! How many integers between 197 and 303 are divisible by 4 or 10?Found 2 solutions by math-vortex, AnlytcPhil:Answer by math-vortex(472)   (Show Source): You can put this solution on YOUR website!Find the first number divisible by 4 starting with 197. 200 is divisible by 4 because 4*50=200. After that, every fourth number if divisible by 4 . 200, 204, 208, 212,..., 300 . 300 is the last number that is divisible by 4 because 4*75=300, and the next integer would be 304. . There are 26 integers in this range; (300-200)/4 is 25, plus 1 extra because we include the numbers at both end of the range. . To find the multiples of 10, we use a similar process. 200 is the first (10*20=200), and 300 is the last (10*30). . 200, 210, 220, 230,..., 300 . There are 11 integers in this range; (300-200)/10 is 10, plus 1 extra because we include the integers at both ends of the range. . That's it. Feel free to email via gmail if this explanation is unclear. . Ms.Figgy math.in.the.vortex@gmail Answer by AnlytcPhil(1321)   (Show Source): You can put this solution on YOUR website!```The other tutor counted the multiples of both 4 and 10 twice. Here's the way I do it. First we find the number of multiple of 4 there are between those two numbers. Multiples of 4 come every fourth number, so to find out how many we do this: There are 303 numbers from 1 to 303. We do not use the 196 numbers from 1 throught 196. So to find out have many numbers there are between 197 and 303, we subtract 303-196 and get 107. Multiples of 4 come every fourth number, So can find out how many there are by dividing 107 by 4 and get 26.75. That doesn't make it to 27, so we use the largest whole number that doesn't exceed that and so we round 26.75 down to 26. That's the number of multiples of 4 between 197 and 303. Now some of those 26 multiples of 4 are also divisible by 10, so the only ones not counted among the 26 are the ones that are multiples of 10 that are not multiples of 4. Since any number of 100's is divisible by 4 we only need to look at the last two digits to find the numbers which are multiples of 10 that are not multiples of 4. They are these five numbers: 10, 30, 50, 70, and 90. So that means 210, 230, 250, 270, and 290 are the only ones between 197 and 303 that are mutiples of 10 that are not multiples of 4. So that's a total of 26+5 or 31. Edwin```