Question

write yes in the blank if the number at the left is divisible by the number at the top. write no in the blank if the number is not divisible by the number at the top.
42
2
3
5
10
...
complete the following table.
42
2
3
5
10

Explanation:

Step1: Check divisibility by 2

A number is divisible by 2 if it's even. 42 is even, so \( 42 \div 2 = 21 \), so divisible. Result: Yes.

Step2: Check divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3. \( 4 + 2 = 6 \), and \( 6 \div 3 = 2 \), so \( 42 \div 3 = 14 \), divisible. Result: Yes.

Step3: Check divisibility by 5

A number is divisible by 5 if it ends in 0 or 5. 42 ends in 2, so \( 42 \div 5 = 8.4 \), not an integer. Result: No.

Step4: Check divisibility by 10

A number is divisible by 10 if it ends in 0. 42 ends in 2, so \( 42 \div 10 = 4.2 \), not an integer. Result: No.

Answer:

For divisor 2: Yes
For divisor 3: Yes
For divisor 5: No
For divisor 10: No

(If filling the table cells corresponding to 42 and divisors 2, 3, 5, 10: the cells would have "Yes", "Yes", "No", "No" respectively.)