SOLUTION: Hi When a number is divided by 3 it gives a remainder of 2. When the same number is divided by 5 it gives a remainder of 3. Find the 2 smallest possible numbers. Thanks

Question 1195075: Hi
When a number is divided by 3 it gives a remainder of 2. When the same number is divided by 5 it gives a remainder of 3. Find the 2 smallest possible numbers.
Thanks
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
When a number is divided by 3 it gives a remainder of 2. When the same number is divided by 5 it gives a remainder of 3. Find the 2 smallest possible numbers.
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8 and 23
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) If it leaves a remainder of 3 when divided by 5, then the units digit is either 3 or 8.

(2) By looking, find the smallest number with units digit 3 or 8 that leaves a remainder of 2 when divided by 3. You should find that number is 8.

(3) Since the divisors 3 and 5 are relatively prime (they have no common factor), all other numbers that satisfy the two conditions will be found by adding multiples of (3*5)=15 to the first number you found.

So the numbers that satisfy both conditions are 8, 23, 38, 53, ...

ANSWER: 8 and 23

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