Number System MCQs with Answers & Explanations

The divisibility rule for 8 is that the number formed by the last three digits must be divisible by 8.

For a number to be divisible by 9, the sum of its digits must be divisible by 9.

**Step 1:** The largest four-digit number is 9999.

The correct answer is D, as the question states the range is between 3 and 60, making option D the only choice that matches this range.

**Step 1:** A number that is divisible by 5, 6, and 7 must be divisible by their Least Common Multiple (LCM).

We count the occurrences of the digit '5' in both the units and tens places.

According to the divisibility rule of 8, a number is divisible by 8 if the number formed by its last three digits is divisible by 8.

**Step 1:** Identify the smallest 5-digit number, which is 10000.

**Step 1:** Let the two consecutive numbers be $x$ and $(x+1)$.

**Step 1:** Divide 231228 by 33 to find the remainder.

Let the two-digit number 'pq' be represented in terms of its place values. The digit 'p' is in the tens place and 'q' is in the units place.

Let the original number be $N$, the divisor be $d$, and the quotient be $q$.

For a number to be divisible by 12, it must be divisible by its co-prime factors, 3 and 4.

- **Greatest six-digit number:** 999,999

To find how many numbers up to 700 are divisible by 17, we simply divide 700 by 17 and take the integer part of the result.

**Step 1:** The smallest 6-digit number is 100000.

Numbers that are divisible by 5 are multiples of 5, meaning they can be divided by 5 without leaving a remainder.

The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. We will check the sum of the digits for each option.

**Step 1:** Apply the rules to each digit of the number 42514563.

We can use modular arithmetic to find the pattern of remainders of powers of 3 when divided by 7.