Question

Determine whether 5, 238 is divisible by 2, 3, 4, 5, 6, 9, or 10.

Answer 1

To determine if 5,238 is divisible by 2, 3, 4, 5, 6, 9, or 10, we can check individual divisibility rules for each number. 5,238 is divisible by 2, 3, 6, and 9, but not divisible by 4, 5, or 10.

Step-by-step explanation:

To determine whether 5,238 is divisible by 2, 3, 4, 5, 6, 9, or 10, we need to check if the number is divisible by each of these individual numbers.

1. For 2, we check if the number is even. Since the last digit of 5,238 is 8, which is even, it is divisible by 2.
2. For 3, we check if the sum of the digits is divisible by 3. The sum of the digits of 5,238 is 5+2+3+8=18, which is divisible by 3. So, it is divisible by 3.
3. For 4, we check if the last two digits form a number divisible by 4. The last two digits of 5,238 are 38, which is not divisible by 4. So, it is not divisible by 4.
4. For 5, we check if the last digit is either 0 or 5. Since the last digit of 5,238 is 8, it is not divisible by 5.
5. For 6, we check if the number is divisible by both 2 and 3. Since it is divisible by 2 and 3, it is divisible by 6.
6. For 9, we check if the sum of the digits is divisible by 9. The sum of the digits of 5,238 is 18, which is divisible by 9. So, it is divisible by 9.
7. For 10, we check if the last digit is 0. Since the last digit of 5,238 is 8, it is not divisible by 10.

In summary, 5,238 is divisible by 2, 3, 6, and 9, but not divisible by 4, 5, or 10.

Answer 2

2, 3, 6

Step-by-step explanation:

Simply try each value using long division.

2:

Since 5,238 ends in an even number, that automatically means it is divisible by 2.

5238/2=2619

Now for 3:

5238/3=1746 no remainder or decimal, so 3 also works

4:

You can either do long division again with 4, or you can see if 5238 divided by 2 (5238/2) is also divisible by 2. Since 2619 doesn't end in an even number, 4 is a no go.

Long division 5238/4=1309.5 decimal here, so 4 isn't an answer

5:

This is also very easy, simply check if the number ends in 0 or 5. Since 5,238 does not, 5 doesn't work either.

6:

You can do the same thing as with 4, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 2. Since 1746 ends in an even number, 6 also works.

Long division: 5238/6=873

9:

You can do the same thing as with 6, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 3.

1746/3=548 with a remainder of 2, which means 9 doesn't work

Long division: 5238/9=548.66 repeating

10:

Finally, 10 is another easy one. Simply check if the number ends in 0. 5,238 does not, so 10 doesn't work.