Can you divide 2 3 5 6 9 10 into 305?

Answer 1

305 can only be [exactly] divided by 5 and not 2, 3, 6, 9 nor 10.

Divisibility tests:

• 2: No

Number must be even (last digit divisible by 2).

Last digit is 5 which is not even, so the whole number (305) not divisible by 2.

• 3: No

Add up the digits of the number; if this sum is divisible by 3, then the original number is divisible by 3:

3 + 0 + 5 = 8 which is not divisible by 3, so the original number (305) is not divisible by 3.

• 5: Yes

Last digit is 0 or 5. Last digit is 5, so 305 is divisible by 5.

• 6: No

6 = 2 x 3, so number must pass both tests for divisibility of 2 and 3; 305 fails tests for (both) 2 and 3 (above), so is not divisible by 6.

• 9: No

Add up the digits of the number; if this sum is divisible by 9, then the original number is divisible by 9:

3 + 0 + 5 = 8 which is not divisible by 9, so the original number (305) is not divisible by 9.

• 10: No

The last digit of the number must be 0. Last digit is 5, so 305 is not divisible by 10.