Divisibility Rule Application for 563607

To determine which number divides 563607, we apply the divisibility rules for each option:

Checking Divisibility by 8

Rule: A number is divisible by 8 if its last three digits form a number divisible by 8.

The last three digits of 563607 are 607.

Calculation: $607 \div 8 = 75$ with a remainder of $7$. Since there is a remainder, 563607 is not divisible by 8.

Checking Divisibility by 3

Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.

Sum of digits: $5 + 6 + 3 + 6 + 0 + 7 = 27$.

Calculation: $27 \div 3 = 9$. Since the sum of the digits (27) is divisible by 3, the number 563607 is divisible by 3.

Checking Divisibility by 13

Rule: One rule involves alternating sums of blocks of three digits from right to left. Another is direct division.

Using direct division: $563607 \div 13 \approx 43354.38$. Since the result is not a whole number, 563607 is not divisible by 13.

Checking Divisibility by 10

Rule: A number is divisible by 10 if its last digit is 0.

The last digit of 563607 is 7.

Therefore, 563607 is not divisible by 10.

Conclusion

Based on the divisibility rules tested, only the number 3 divides 563607 evenly.