If a 7-digit number 87321A6 is completely divisible by 6, what is the least value of A?
0
A number is divisible by 6 only if it is divisible by both 2 and 3.
The number 87321A6 already ends in 6, an even digit, so it is always divisible by 2 regardless of the value of A.
For divisibility by 3, the sum of all digits must be divisible by 3: 8 + 7 + 3 + 2 + 1 + A + 6 = 27 + A, so 27 + A must be a multiple of 3.
Since 27 is already divisible by 3, the smallest digit A that keeps 27 + A divisible by 3 is A = 0, because 27 + 0 = 27, which is divisible by 3.
Hence, the least value of A for which 87321A6 is divisible by 6 is 0.
Similar Questions
Which of the following numbers is divisible by both 2 and 5?
Find the smallest digit value for A such that 58A4 is divisible by 4.
If a 7-digit number 91056A4 is completely divisible by 3, what is the least value of A?
If a 7-digit number 65873A8 is completely divisible by 22, what is the value of A?
If a 7-digit number 48085A7 is completely divisible by 3, what is the least value of A?
Find the smallest number that should be added to 97306 to make it divisible by 6.
What is the value that must be assigned to A so that the 8-digit number 378A6070 is divisible by 18?
What is the value that must be assigned to A so that the 8-digit number 753A3228 is divisible by 18?
What is the least value that must be assigned to A so that the 8-digit number 910A3076 is divisible by 6?
What is the value that must be assigned to A so that the 8-digit number 541A4888 is divisible by 9?
Important Questions from Divisibility and Remainder
If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
