A 6-digit number has digits as consecutive natural numbers. The number is always divisible by:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
A number is divisible by 3 when the sum of its digits is divisible by 3. Six consecutive digits, in either order, are \(a,\ a+1,\ a+2,\ a+3,\ a+4,\ a+5\).
Sum of the digits \(=6a+15=3(2a+5)\)
This is always a multiple of 3, so the number is always divisible by 3
The other divisors fail for some such number: 234567 is odd, so it is not divisible by 2 or 4, and 123456 does not end in 0 or 5, so it is not divisible by 5.