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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 43197 is divided by 7
a 2
b 4
c 6
d 1
Answers (2)
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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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1. 517xy is number and 89 is divisor. So, let us take 51700 as a number. So, 51700/89 = 89x58+80. So, the number less than 51700 that would be divisible by 89 would be 51620.
So, next number would be 51620+89 = 51709.
next, 51709+89=51798.
Now, if we add further, then it the format of the number would be 518xy, which we don't want.
So, the answer is 51709 and 51798.