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1777 has exactly 5 digits when converted to base 'x' from the decimal system. What is the minimum possible value of x?

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Important Questions on Number Systems

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What will be the sum of all natural numbers between 101 and  1000 which on division by 2, 4, 6, 8, 10 leave remainders 1, 3, 5, 7, 9 respectively?
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Unit digit of which of the following is the same as the units digits of a17+b17For any positive integer value of a,b?
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How many 4 Digit numbers are there in the decimal system, which have exactly 4 Digits when expressed in Base 6, Base 7, Base 8?
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What is the difference between the highest and the least four digit natural numbers that have exactly four digits when expressed in Base 6 and Base 7.
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If n is a natural number, then what is the sum of all the possible distinct remainders when 9n+6n+4n+11n is divided by 10?
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If x, y, z and w are natural numbers, then what is the sum of all the possible remainders when 9x+6y+4z+11z is divided by 10?
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What is the maximum possible sum of the number of Mondays and Thursdays in two consecutive years?
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In the previous question find the minimum possible sum of the number of Mondays and Thursdays in two consecutive years?