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It is 199.

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Q: What is the greatest number which on dividing 3784 and 9157 leave 3 as remainder in each?
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What is the greatest no which divides 1675 and 2037 leaving a remainder 6 and 5 respectively?

There is no such number. 1675 - 6 = 1669 which is a prime. As a result, the only number that can divide it is 1 and 1669 itself. However, 1 not only divides 1669 but it also divides 1675. That is, 1 does not leave a remainder of 6 when dividing 1675.


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A prime number is a number that can only be divided by 1 or itself. A composite number is a number which can be divided by a number other than itself or 1 and not leave a remainder. 178 divided by 2, for example, equals 89 (89 + 89 = 178). Since 2 is not dividing 178 by 1 or by itself and leaves no remainder, it is a composite number.


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