1. Which whole numbers, greater than 1, divide evenly into all of the nine 3-digit numbers:
111, 222, 333, 444 ...... 999 ?
2. how many odd numbers less than 500 are exactly divisible by 7 ?
3. what is the smallest number which, when divided by 3,4,5 or 6, always leaves a remainder of 1 ?
2006-11-20 14:19:01 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1. its 55.5---to get even no.111/2=55.5
2.71 ---500/7 = 71.42 ...and 497 is the last term divisible by 7
so.... the total no is 71
3.61 = lcm of 3,4,5,6 is 60 then add 1
2006-11-20 14:46:33 · answer #1 · answered by smith 3 · 0⤊ 0⤋
1) 3 is the only number that divides all the given numbers evenly. This is because 111/3 =37 which is prime.
2) 7, 21, 35, 49, ....... 7+14n
7+14n =500
n = 493/14= 35.2
Therefore there are 36 such numbers, since n starts with 0.
The least common multiple of 3,4,5,6 is 60. Therefore 61 when divided by any of the given numbers will leave a remainder of 1.
2006-11-20 14:48:43 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
3) (S-1) is the LCM of 3,4,5,6
thus S-1 = 3 * 2^2 * 5 = 60 = > S = 61
2006-11-20 14:24:22 · answer #3 · answered by James Chan 4 · 0⤊ 0⤋