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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Q: What is the smallest number that leaves a remainder of 1 when divided by 2 and a remainder of 2 when divided by 3?

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62 is the smallest number that leaves a remainder of 2 when divided by 3, 4, 5, and 6.

119

0.25

23

Try 30

64 and 76

A number leaves reminder 6 when divided by 10. What is the remainder when the number is divided by 5? Justify your reasoning.

36 divided by 28 would be 1 remainder 8and44 divided by 32 would be 1 remainder 12

0.6667

12 is the smallest whole number that gives a remainder of 4 when it is divided by 8.

12*1 + 3 = 15 12*2 + 3 = 27 12*4 + 3 = 51 when 51 divided by 15 gives the remainder as 6.

24

5

It is a factor of that number and leaves no remainder

24

209

26

103

11

85. A number when divided by 238, leaves a remainder 79. What will be the remainder when the number is divided bv 17 ? (1) 8 (2) 9 (3) 10 @) 11

The answer is 8.

0.8

7

L.C.M of 17 and 29 is 493.493 + 3 = 496Answer = 496

It is any number which, when divided by 2, leaves no remainder.

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What is the smallest number that leaves a remainder of 1 when divided by 2 and a remainder of 2 when divided by 3?

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