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Doubt & Answer Explanation

Doubt

1) Find all numbers of the form 517xy that are divisible by 89.

2) Find the remainder which 73 75 78 57 197 is divided by 34
a.34
b.30
c.15
d.28

3)Find the remainder when 73x75x78x57x197 is divisible by 34
a.32
c.30
c.15
d.28

4)Find the remainder when 73x75x78x57x197x37 is divided by 34
a.32
b.30
c.15
d.28

5)find the remainder when 43¹⁹⁷is divided by 7
a 2
b 4
c 6
d 1

Answer Explanation

43¹⁹⁷
= (42 + 1)¹⁹⁷

Remainder when it is divided by 7 is 1 as 42 is divisible by 7.

73x75x78x57x197x37

Divide each number by 34 and see the remainder

73 when divided by 34 leaves remainder = 5
75 when divided by 34 leaves remainder = 7
78 when divided by 34 leaves remainder = 10
57 when divided by 34 leaves remainder = 23
197 when divided by 34 leaves remainder = 27
37 when divided by 34 leaves remainder = 3

Thus remainder will be same as when 5x7x10x23x27x3 is divided by 34

or 35x230x81 is divided by 34

35 when divided by 34 leaves remainder = 1
230 when divided by 34 leaves remainder = 26
81 when divided by 34 leaves remainder = 13

So remainder is same as when 1x26x13 divided by 34

or when 338 divided by 13

remainder = 32

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