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The number 35a246772 is in base 9. This number when written in base 10 is divisible by 8. Find the value of digit a.
Correct answer is '4'. Can you explain this answer?
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The number 35a246772 is in base 9. This number when written in base 10...
(35a246772)9
= (3 x 98) + (5 x 97) + (a x 96) + ... + (2 x 90)
= [3 x (8 + 1)8] + [5 x (8 + 1)7] + [a x (8 + 1)6] + ... + [2 x (8 + 1)6]
When the above expression is expanded, only the last term of each binomial expression is not divisible by 8.
Thus, the number will be divisible when sum of its digits is divisible by 8. Sum of digits = 3 + 5 + <z + 2 + 4 + 6 + 7 + 7 + 2 = 36 + a The sum will be divisible by 8 when a = 4.
Answer: 4
Thus, the number will be divisible when sum of its digits is divisible by 8. Sum of digits = 3 + 5 + <z + 2 + 4 + 6 + 7 + 7 + 2 = 36 + a The sum will be divisible by 8 when a = 4.
Answer: 4
Most Upvoted Answer
The number 35a246772 is in base 9. This number when written in base 10...
N is a number in base 9.Find N when n is divided by 8(in base 10)? And N can be very large.say N=32323232....50 digits
This can be done by converting N to base 10.But time consuming.
What will be the fastest approach given that no proof is required.Like in a rapid fire round. Just Answer.
One solution is: In base 9,divisibility check for 8 is sum of the digits(digit sum).Digit sum of N=25(i.e from 25*3+25*2).Converting 25 to base 10 gives 23.Thus the question changes to (23*2+23*2) in base 10 i.e 115 in base 10.COnverting it back to base 9 gives 137.Now sum of digit in base 9 is 1+3+7 i.e 12.So answers is (1+2%8)=3
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Community Answer
The number 35a246772 is in base 9. This number when written in base 10...
Conversion to Base 10
To find the value of digit a in the number 35a246772, we first need to convert the number from base 9 to base 10.
To convert a number from base 9 to base 10, we use the following formula:
(number in base 10) = a[n] * 9^n + a[n-1] * 9^(n-1) + ... + a[0] * 9^0
Where n is the number of digits in the number and a[i] represents the value of the ith digit.
Divisibility by 8
Next, we are given that the number in base 10 is divisible by 8. To check the divisibility of a number by 8, we need to determine if the number is a multiple of 8.
A number is divisible by 8 if the last three digits of the number form a multiple of 8. In other words, if the remainder of the division of the last three digits by 8 is zero, then the number is divisible by 8.
Solving the Problem
Let's start by converting the number from base 9 to base 10:
35a246772 = 3*9^9 + 5*9^8 + a*9^7 + 2*9^6 + 4*9^5 + 6*9^4 + 7*9^3 + 7*9^2 + 2*9^1
Since we are given that the number is divisible by 8, we can look at the last three digits (772) and check if they form a multiple of 8.
772 = 7*9^2 + 7*9^1 + 2*9^0 = 567 + 63 + 2 = 632
To verify if 632 is divisible by 8, we can check if the remainder of 632/8 is zero.
632/8 = 79 remainder 0
Therefore, the number 35a246772 is divisible by 8, and the value of digit a is 4.
To find the value of digit a in the number 35a246772, we first need to convert the number from base 9 to base 10.
To convert a number from base 9 to base 10, we use the following formula:
(number in base 10) = a[n] * 9^n + a[n-1] * 9^(n-1) + ... + a[0] * 9^0
Where n is the number of digits in the number and a[i] represents the value of the ith digit.
Divisibility by 8
Next, we are given that the number in base 10 is divisible by 8. To check the divisibility of a number by 8, we need to determine if the number is a multiple of 8.
A number is divisible by 8 if the last three digits of the number form a multiple of 8. In other words, if the remainder of the division of the last three digits by 8 is zero, then the number is divisible by 8.
Solving the Problem
Let's start by converting the number from base 9 to base 10:
35a246772 = 3*9^9 + 5*9^8 + a*9^7 + 2*9^6 + 4*9^5 + 6*9^4 + 7*9^3 + 7*9^2 + 2*9^1
Since we are given that the number is divisible by 8, we can look at the last three digits (772) and check if they form a multiple of 8.
772 = 7*9^2 + 7*9^1 + 2*9^0 = 567 + 63 + 2 = 632
To verify if 632 is divisible by 8, we can check if the remainder of 632/8 is zero.
632/8 = 79 remainder 0
Therefore, the number 35a246772 is divisible by 8, and the value of digit a is 4.
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The number 35a246772 is in base 9. This number when written in base 10 is divisible by 8. Find the value of digit a.Correct answer is '4'. Can you explain this answer?
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