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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. 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?

  2. As nine-digit number 89563x87y is divisible by 72. What is the value of \(\sqrt{7x-3y}\)  ?

  3. The greatest number that on dividing 2675 and 2320 leaves the reminder 5 and 6 ,respectively is : 

  4. Find the greatest number that exactly divides 2880, 6525 and 8307.

  5. If a 10 - digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest value of y is :

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