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No number can satisfy these conditions: To have a remainder of 1 when divided by 6, the number must be odd (as all multiples of 6 are even and an even number plus 1 is odd) To have a remainder of 2 when divided by 8, the number must be even (as all multiples of 8 are even and an even number plus 2 is even) No number is both odd and even. → No number exists that has a remainder of 1 when divided by 6, and 2 when divided by 8.
301 is one such number.
7, 37, 67, 97, 127, and an infinite number of other numbers in this series (starting with 7 and increasing in increments of 30) have a remainder of 1 when divided by 6 and a remainder of 2 when divided by 5.
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