Divisibility Check for 36
To determine if a number is divisible by 36, we need to check if it's divisible by both 4 and 9, as 36 can be factored into $36 = 4 \times 9$, and 4 and 9 share no common factors other than 1.
Divisibility Rules
Let's recall the divisibility rules we'll use:
- Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Analyzing the Options
We will now examine each option to see if it meets both criteria.
| Number | Last Two Digits | Divisible by 4? | Sum of Digits | Divisible by 9? | Divisible by 36? |
|---|---|---|---|---|---|
| 1542 | 42 | No (42 ÷ 4 = 10.5) | $1 + 5 + 4 + 2 = 12$ | No (12 ÷ 9 = 1.33...) | No |
| 96272 | 72 | Yes (72 ÷ 4 = 18) | $9 + 6 + 2 + 7 + 2 = 26$ | No (26 ÷ 9 = 2.88...) | No |
| 55512 | 12 | Yes (12 ÷ 4 = 3) | $5 + 5 + 5 + 1 + 2 = 18$ | Yes (18 ÷ 9 = 2) | Yes |
| 8840 | 40 | Yes (40 ÷ 4 = 10) | $8 + 8 + 4 + 0 = 20$ | No (20 ÷ 9 = 2.22...) | No |
Conclusion
From the analysis:
- 1542 is not divisible by 4 or 9.
- 96272 is divisible by 4 but not by 9.
- 55512 is divisible by both 4 (since 12 is divisible by 4) and 9 (since the sum of its digits, 18, is divisible by 9).
- 8840 is divisible by 4 but not by 9.
Therefore, the only number among the options that is divisible by 36 is 55512.
Similar Questions
- The number 1254216 is divisible by which of the following numbers?
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- The five-digit number 725yz is divisible by 15. What is the maximum possible value of the product of y and z?
Important Questions from Divisibility and Remainder
What is the sum of the digits of the least number which when divided by 12, 16 and 20 leaves the same remainder 6 in each case and it is divisible by 9?
As nine-digit number 89563x87y is divisible by 72. What is the value of \(\sqrt{7x-3y}\) ?
The greatest number that on dividing 2675 and 2320 leaves the reminder 5 and 6 ,respectively is :
Find the greatest number that exactly divides 2880, 6525 and 8307.
If a 10 - digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest value of y is :
