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Q: What is the smallest number that can be divided into 5 with a remainder of 3?

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The smallest number that can be divided by 2 3 4 5 6 7 8 and always give you a remainder of 1 is 841

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5. To leave a remainder of 1 when divided by 2, the number must be odd. To leave a remainder of 2 when divided by 3, the number must also be two more than a multiple of 3. The multiples of 3 which are odd are 1 x 3, 3 x 3, 5 x 3, etc. The smallest odd multiple of three is 1 x 3 = 3 ⇒ required number is 3 + 2 = 5.

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Try 23

169 is the smallest such number.

A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.A modulus is the remainder after a number has been divided into another. 3 divides into 10 with a remainder of 1. So 1 is the modulus of 10 divided by 3.

It will be 3.

The answer is 1. The smallest prime is 2 and the greatest prime (of however many digits) must be odd. The remainder of ANY odd number when divided by 2 must be 1.

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