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Question

The number 56890065 is completely divisible by only:

The correct answer is

3

The problem requires determining which number completely divides 56890065 from the given options. To solve this, we need to apply divisibility rules.

Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. For 56890065, the sum of digits is 5+6+8+9+0+0+6+5 = 39. Since 39 is not divisible by 9, 56890065 is not divisible by 9.

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits, 39, is divisible by 3 (39 ÷ 3 = 13). Therefore, 56890065 is divisible by 3.

Divisibility by 11 and 4: For 11, the rule is alternating sum of digits should be divisible by 11. Alternating sum: (5-6+8-9+0-0+6-5) = -1, which is not divisible by 11. For 4, the last two digits, 65, are not divisible by 4. Therefore, 56890065 is not divisible by both 11 and 4.

Divisibility by 6 and 7: A number is divisible by 6 if divisible by both 2 and 3. 56890065 is not divisible by 2 (it's odd). Also, no individual test needed for 7 as 56890065 is not divisible by 6. Combined divisible by 6 and 7 is not possible here.

Thus, 56890065 is completely divisible by 3.

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Important Questions from Divisibility and Remainder

  1. If a five digit number 247xy is divisible by 3, 7 and 11, then what is the value of (2y - 8x)?

  2. If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x + 3y) for x ≠ y ?

  3. Find the greatest value of b so that 30a68b (a > b) is divisible by 11.

  4. What is the remainder when the product of 335, 608 and 853 is divided by 13?

  5. What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
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