Question

A number G236G0 can be divided by 36 if G is:

• A. 8
• B. 6
• C. 1
• D. More than one values are possible.

Answer 1

The Correct Option is A

To determine the value of G for which the number G236G0 is divisible by 36, we need to consider the divisibility rules for both 4 and 9, since 36 = 4 × 9.

Step 1: Check Divisibility by 4

A number is divisible by 4 if the last two digits form a number that is divisible by 4. Here, the last two digits are "G0", which means they form the number 10G. This simplifies to ensuring 0G is divisible by 4, which leads to 10*G being the relevant calculation.

Possible digits for G are 0, 2, 4, 6, and 8 because 00, 20, 40, 60, and 80 are divisible by 4. However, because G appears twice in the number, we need G such that both digits fulfill divisibility together, continuing to the verification: potentially reach numbers are 0, 2, 4, 6, 8.

Step 2: Check Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9. For the number G236G0, the sum of its digits is G + 2 + 3 + 6 + G + 0 = 2G + 11. This must be divisible by 9.

Now, test the values found in step 1:

• For G = 0: 2(0) + 11 = 11 (Not divisible by 9)
• For G = 2: 2(2) + 11 = 15 (Not divisible by 9)
• For G = 4: 2(4) + 11 = 19 (Not divisible by 9)
• For G = 6: 2(6) + 11 = 23 (Not divisible by 9)
• For G = 8: 2(8) + 11 = 27 (Divisible by 9)

The only value of G that works for both divisibility conditions is 8.

Conclusion

The number G236G0 can be divided by 36 if G is 8.