Q. 1.2 - Intermediate Algebra

Question

Is 3,765 divisible by (a) 2? (b) 3? (c) 5? (d) 6? (e) 10? 

Step-by-Step Solution

Answer

The number 3,765 is divisible by options (b) 3 and (c) 5.

Step 1. Given information

The given number is 3,765.

We have to check, by which number 4,962 is divisible out of the given options.

Step 2. Checking for option (a)

The number 3,765 does not end with 0, 2, 4, 6 or 8.

Therefore, it is not divisible by 2. 

Step 3. Checking for option (b)

The sum of the digits of 3,765 is 

3+7+6+5=21

21 is divisible by 3.

Thus, 3,765 is divisible by 3.

Step 4. Checking for option (c)

The number 3,765 ends with 5.

Therefore, it is divisible by 5.

Step 5. Checking for option (d)

The number is divisible by both 3 and but not 2.

Therefore, 3,765 is not divisible by 6.

Step 6. Checking for option (e)

The number 3,765 does not end with 0.

Therefore, it is not divisible by 10.

Step 7. Conclusion

From the above steps, we can observe that the given number 3,765 is divisible by 3 and 5. 

Therefore, the correct options will be (b), and (c).